Speed of gravity - Knowledge (XXG)

996: 1622:

with unchanging velocity), the orbital results calculated by general relativity are the same as those of Newtonian gravity with instantaneous action at a distance, because they are modelled by the behavior of a static field with constant-velocity relative motion, and no aberration for the forces involved. Although the calculations are considerably more complicated, one can show that a static field in general relativity does not suffer from aberration problems as seen by an unaccelerated observer (or a weakly accelerated observer, such as the Earth). Analogously, the "static term" in the electromagnetic

1257: 1172:

move with respect to a distant charge. Thus, constant motion of an observer with regard to a static charge and its extended static field (either a gravitational or electric field) does not change the field. For static fields, such as the electrostatic field connected with electric charge, or the gravitational field connected to a massive object, the field extends to infinity, and does not propagate. Motion of an observer does not cause the direction of such a field to change, and by symmetrical considerations, changing the observer frame so that the charge appears to be moving at a constant rate,

1314:, which is the travel time of gravity from the sun to the Earth times the relative velocity of the sun and the Earth. As seen in Fig. 1, the pull of gravity (if it behaved like a wave, such as light) would then always be displaced in the direction of the Earth's velocity, so that the Earth would always be pulled toward the optical position of the Sun, rather than its actual position. This would cause a pull ahead of the Earth, which would cause the orbit of the Earth to spiral outward. Such an outspiral would be suppressed by an amount 1207:, according to which, when the mass distribution of a system changes, its gravitational field instantaneously adjusts. Therefore, the theory assumes the speed of gravity to be infinite. This assumption was adequate to account for all phenomena with the observational accuracy of that time. It was not until the 19th century that an anomaly in astronomical observations which could not be reconciled with the Newtonian gravitational model of instantaneous action was noted: the French astronomer 326: 1009: 1580:

body continued with constant velocity. This effect causes the distant fields of unaccelerated moving charges to appear to be "updated" instantly for their constant velocity motion, as seen from distant positions, in the frame where the source-object is moving at constant velocity. However, as discussed, this is an effect which can be removed at any time, by transitioning to a new

1395:, i.e. practically the speed of light. But Gerber's derivation of the formula was faulty, i.e., his conclusions did not follow from his premises, and therefore many (including Einstein) did not consider it to be a meaningful theoretical effort. Additionally, the value it predicted for the deflection of light in the gravitational field of the sun was too high by the factor 3/2. 1180:

remains true if the charged bodies and their observers are made to "move" (or not), by simply changing reference frames. This fact sometimes causes confusion about the "speed" of such static fields, which sometimes appear to change infinitely quickly when the changes in the field are mere artifacts of the motion of the observer, or of observation.

1579:

In other words, since the gravitoelectric field is, by definition, static and continuous, it does not propagate. If such a source of a static field is accelerated (for example stopped) with regard to its formerly constant velocity frame, its distant field continues to be updated as though the charged

1479:

What would happen if we could communicate by signals other than those of light, the velocity of propagation of which differed from that of light? If, after having regulated our watches by the optimal method, we wished to verify the result by means of these new signals, we should observe discrepancies

1427:

that the attraction of opposite charged particles is stronger than the repulsion of equal charged particles. The resulting net force is exactly what is known as universal gravitation, in which the speed of gravity is that of light. This leads to a conflict with the law of gravitation by Isaac Newton,

1788:

in two — one for gravity and another one for light — the authors claimed that Asada's claim was theoretically unsound. The two null cones overlap in general relativity, which makes tracking the speed-of-gravity effects difficult and requires a special mathematical technique of gravitational retarded

1721:

setting, measuring the speed of gravity by comparing theoretical results with experimental results will depend on the theory; use of a theory other than that of general relativity could in principle show a different speed, although the existence of gravitational damping at all implies that the speed

1783:

Kopeikin and Fomalont, however, continue to vigorously argue their case and the means of presenting their result at the press conference of the American Astronomical Society (AAS) that was offered after the results of the Jovian experiment had been peer-reviewed by the experts of the AAS scientific

1807:

in 2017, the finale of a neutron star inspiral observed through both gravitational waves and gamma rays, at a distance of 130 million light years, currently provides by far the best limit on the difference between the speed of light and that of gravity. Photons were detected 1.7 seconds after

1575:

the (now moving) emitting body's field lines must not at a distance be retarded or aberred. Moving charged bodies (including bodies that emit static gravitational fields) exhibit static field lines that do not bend with distance and show no speed of light delay effects, as seen from bodies moving

1322:

must be very large. As is now known, it may be considered to be infinite in the limit of straight-line motion, since as a static influence it is instantaneous at distance when seen by observers at constant transverse velocity. For orbits in which velocity (direction of speed) changes slowly, it is

1227:

in 1805. Based on Newton's force law he considered a model in which the gravitational field is defined as a radiation field or fluid. Changes in the motion of the attracting body are transmitted by some sort of waves. Therefore, the movements of the celestial bodies should be modified in the order

1171:

should not be confused with "changes" in the behavior of static fields that are due to pure observer-effects. These changes in direction of a static field are, because of relativistic considerations, the same for an observer when a distant charge is moving, as when an observer (instead) decides to

1130:

is a conversion factor for changing the unit of time to the unit of space. This makes it the only speed which does not depend either on the motion of an observer or a source of light and / or gravity. Thus, the speed of "light" is also the speed of gravitational waves, and further the speed of any

1621:

of gravity that Newton was originally concerned with, because there is no such aberration in static field effects. Because the acceleration of the Earth with regard to the Sun is small (meaning, to a good approximation, the two bodies can be regarded as traveling in straight lines past each other

1268:

with violation of conservation of energy and of angular momentum. In 1776, Laplace considered a different mechanism whereby gravity is caused by "the impulse of a fluid directed towards the centre of the attracting body". In such a theory, a finite speed of gravity results in the Earth spiraling

1326:

The attraction toward an object moving with a steady velocity is towards its instantaneous position with no delay, for both gravity and electric charge. In a field equation consistent with special relativity (i.e., a Lorentz invariant equation), the attraction between static charges moving with

1183:

In such cases, nothing actually changes infinitely quickly, save the point of view of an observer of the field. For example, when an observer begins to move with respect to a static field that already extends over light years, it appears as though "immediately" the entire field, along with its

1179:

The consequence of this is that static fields (either electric or gravitational) always point directly to the actual position of the bodies that they are connected to, without any delay that is due to any "signal" traveling (or propagating) from the charge, over a distance to an observer. This

1184:

source, has begun moving at the speed of the observer. This, of course, includes the extended parts of the field. However, this "change" in the apparent behavior of the field source, along with its distant field, does not represent any sort of propagation that is faster than light.

1779:

It is important to keep in mind that none of the debaters in this controversy are claiming that general relativity is "wrong". Rather, the debated issue is whether or not Kopeikin and Fomalont have really provided yet another verification of one of its fundamental predictions.

1248:

as it does in modern theories. This led Laplace to conclude that the speed of gravitational interactions is at least 7×10 times the speed of light. This velocity was used by many in the 19th century to criticize any model based on a finite speed of gravity, like electrical or

1761:. Kopeikin and Fomalont concluded that the speed of gravity is between 0.8 and 1.2 times the speed of light, which would be fully consistent with the theoretical prediction of general relativity that the speed of gravity is exactly the same as the speed of light. 1432:

that a finite speed of gravity leads to some sort of aberration and therefore makes the orbits unstable. However, Lorentz showed that the theory is not concerned by Laplace's critique, because due to the structure of the Maxwell equations only effects in the order

1544:

Suddenly displacing one of two gravitoelectrically interacting particles would, after a delay corresponding to lightspeed, cause the other to feel the displaced particle's absence: accelerations due to the change in quadrupole moment of star systems, like the

1327:

constant relative velocity is always toward the instantaneous position of the charge (in this case, the "gravitational charge" of the Sun), not the time-retarded position of the Sun. When an object is moving in orbit at a steady speed but changing velocity

1496:; here, on the contrary, this hypothesis is conjoined with many others, and it may be that between them a more or less perfect compensation takes place. The application of the Lorentz transformation has already provided us with numerous examples of this. 1559:

Two gravitoelectrically interacting particle ensembles, e.g., two planets or stars moving at constant velocity with respect to each other, each feel a force toward the instantaneous position of the other body without a speed-of-light delay because

1368:. Those theories are not invalidated by Laplace's critique, because although they are based on finite propagation speeds, they contain additional terms which maintain the stability of the planetary system. Those models were used to explain the 1480:

due to the common translatory motion of the two stations. And are such signals inconceivable, if we take the view of Laplace, that universal gravitation is transmitted with a velocity a million times as great as that of light?

1281:

invariance of static fields, Laplace assumed that when an object like the Earth is moving around the Sun, the attraction of the Earth would not be toward the instantaneous position of the Sun, but toward where the Sun

397: 1637:

It is in fact not very easy to construct a self-consistent gravity theory in which gravitational interaction propagates at a speed other than the speed of light, which complicates discussion of this possibility.

1685:

For the reader who desires a deeper background, a comprehensive review of the definition of the speed of gravity and its measurement with high-precision astrometric and other techniques appears in the textbook

1445:

The special form of these terms may perhaps be modified. Yet, what has been said is sufficient to show that gravitation may be attributed to actions which are propagated with no greater velocity than that of

1717:") can be measured, and since it depends on the speed of gravity, comparing the measured values to theory shows that the speed of gravity is equal to the speed of light to within 1%. However, according to 1454:

examined the gravitational theory of Lorentz and classified it as compatible with the relativity principle, but (like Lorentz) he criticized the inaccurate indication of the perihelion advance of Mercury.

1795:

also showed that the experiment did not actually measure the speed of gravity because the effects were too small to have been measured. A response by Kopeikin and Fomalont challenges this opinion.

1603:

transmit quantized (discrete) information, i.e., it could not constitute a well-ordered series of impulses carrying a well-defined meaning (this is the same for gravity and electromagnetism).

767: 1387:, who derived in 1898 the identical formula, which was also derived later by Einstein for the perihelion advance. Based on that formula, Gerber calculated a propagation speed for gravity of 2867:

Kopeikin, S.M. & Mashhoon, B. (2002). "Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies".

1776:

in a paper to the Astrophysical Journal Letters theorized that the proposed experiment was essentially a roundabout confirmation of the speed of light instead of the speed of gravity.

1556:

approximation. In the following discussion the diagonal components of the tensor would be termed gravitoelectric components, and the other components will be termed gravitomagnetic.

1076:

of matter results in subsequent alteration, at a distance, of the gravitational field which it produces. In the relativistic sense, the "speed of gravity" refers to the speed of a

1492:

Laplace showed in effect that the propagation is either instantaneous or much faster than that of light. However, Laplace examined the hypothesis of finite propagation velocity

1040: 3251:

Bettoni, Dario; Ezquiaga, Jose María; Hinterbichler, Kurt & Zumalacárregui, Miguel (2017-04-14). "Speed of gravitational waves and the fate of scalar-tensor gravity".

1484:

However, in 1905 Poincaré calculated that changes in the gravitational field can propagate with the speed of light if it is presupposed that such a theory is based on the

419: 1155:(which are the presumptive field particles associated with gravity; however, an understanding of the graviton, if it exists, requires an as-yet unavailable theory of 2570: 1199:

law requires that each particle with mass respond instantaneously to every other particle with mass irrespective of the distance between them. In modern terms,

1541:(GR), effects like those of Newtonian gravitation (it does not depend on the existence of gravitons, mentioned above, or any similar force-carrying particles). 1176:

does not cause the direction of its field to change, but requires that it continue to "point" in the direction of the charge, at all distances from the charge.

624: 1772:, have criticized these claims on the grounds that they have allegedly misinterpreted the results of their measurements. Notably, prior to the actual transit, 4264:

Kopeikin, Sergei & Fomalont, Edward (2007). "Gravimagnetism, Causality, and Aberration of Gravity in the Gravitational Light-Ray Deflection Experiments".

2366: 1808:

peak gravitational wave emission; assuming a delay of zero to 10 seconds, the difference between the speeds of gravitational and electromagnetic waves,

1549:, have removed much energy (almost 2% of the energy of our own Sun's output) as gravitational waves, which would theoretically travel at the speed of light. 977: 787: 629: 742: 3146:

Lombriser, Lucas & Lima, Nelson (2017). "Challenges to self-acceleration in modified gravity from gravitational waves and large-scale structure".

3373:

Sakstein, Jeremy & Jain, Bhuvnesh (16 October 2017). "Implications of the neutron star merger GW170817 for cosmological scalar-tensor theories".

1033: 1256: 1713:. The orbits of these binary pulsars are decaying due to loss of energy in the form of gravitational radiation. The rate of this energy loss (" 1250: 655: 489: 2814:

Kopeikin, S.M. & Schaefer, G. (1999). "Lorentz covariant theory of light propagation in gravitational fields of arbitrary-moving bodies".

995: 3763:

Kopeikin, Sergei M. (2004). "The Speed of Gravity in General Relativity and Theoretical Interpretation of the Jovian Deflection Experiment".

2190: 2161: 2031: 1949: 694: 332: 1626:

theory of the fields from a moving charge does not suffer from either aberration or positional-retardation. Only the term corresponding to

1509: 4037:

Kopeikin, Sergei M. (2005). "Comment on 'Model-dependence of Shapiro time delay and the "speed of gravity/speed of light" controversy".

1026: 3943:

Kopeikin, Sergei & Fomalont, Edward (2006). "Aberration and the Fundamental Speed of Gravity in the Jovian Deflection Experiment".

1826: 1571:

in a static field emanating from a "motionless body" therefore means Lorentz invariance requires that in the previously moving body's

1416: 1261: 406: 1623: 1612: 1352:

At the end of the 19th century, many tried to combine Newton's force law with the established laws of electrodynamics, like those of

1057: 432: 2761:

Kopeikin, S.M. & Fomalont, E.B. (2006). "Aberration and the fundamental speed of gravity in the Jovian deflection experiment".

1784:

organizing committee. In a later publication by Kopeikin and Fomalont, which uses a bi-metric formalism that splits the space-time

712: 1424: 325: 3639:

Fomalont, E. B. & Kopeikin, Sergei M. (2003). "The Measurement of the Light Deflection from Jupiter: Experimental Results".

3225: 4436: 1789:

potentials, which was worked out by Kopeikin and co-authors but was never properly employed by Asada and/or the other critics.

619: 1838: 1537:

should exist and propagate as a wave at lightspeed: a slowly evolving and weak gravitational field will produce, according to

4225:

Kopeikin, Sergei (2006). "Comments on the paper by S. Samuel "On the speed of gravity and the Jupiter/Quasar measurement"".

752: 3498:

Kopeikin, Sergei M. (2001). "Testing Relativistic Effect of Propagation of Gravity by Very-Long Baseline Interferometry".

2655:

Fomalont, Ed & Kopeikin, Sergei (2003). "The measurement of the light deflection from Jupiter: Experimental results".

706: 414: 2322: 1564:

demands that what a moving body in a static field sees and what a moving body that emits that field sees be symmetrical.

772: 3686:

Kopeikin, Sergei M. (Feb 21, 2003). "The Measurement of the Light Deflection from Jupiter: Theoretical Interpretation".

1105: 3990:

Carlip, Steven (2004). "Model-Dependence of Shapiro Time Delay and the "Speed of Gravity/Speed of Light" Controversy".

4475: 4470: 1420: 1369: 1318:

compared to the force which keeps the Earth in orbit; and since the Earth's orbit is observed to be stable, Laplace's

1212: 1013: 504: 424: 1617:

The finite speed of gravitational interaction in general relativity does not lead to the sorts of problems with the

1600: 1468: 1380:

and Riemann, whereby the speed of gravity is equal to the speed of light. However, those hypotheses were rejected.

917: 465: 717: 2516:

Carlip S (2004). "Model-Dependence of Shapiro Time Delay and the "Speed of Gravity/Speed of Light" Controversy".

1792: 1260:

Figure 1. One possible consequence of combining Newtonian Mechanics with a finite speed of gravity. If we assume

529: 3093:

Lombriser, Lucas & Taylor, Andy (28 September 2015). "Breaking a dark degeneracy with gravitational waves".

1830: 792: 2071:"Lettre de M. Le Verrier à M. Faye sur la théorie de Mercure et sur le mouvement du périhélie de cette planète" 1441:

arise. But Lorentz calculated that the value for the perihelion advance of Mercury was much too low. He wrote:

952: 942: 609: 267: 1546: 671: 2211: 1655: 1588: 1553: 1534: 1513: 1472: 937: 1126:

is not only about light; instead it is the highest possible speed for any interaction in nature. Formally,

737: 2051: 1971: 1485: 907: 892: 499: 3701:

Kopeikin, Sergei M. (2003). "The Post-Newtonian Treatment of the VLBI Experiment on September 8, 2002".

2401: 1714: 1670: 1596: 1377: 1200: 1168: 1148: 882: 450: 1834: 4415: 2294: 1634:

in the Liénard–Wiechert potential shows a direction toward the time-retarded position of the emitter.

1552:

In GR gravity is described by a 4x4 tensor, which, in the weak gravity limit, can be described by the

4381: 4334: 4311:

Kopeikin, Sergei & Fomalont, Edward (2008). "Radio interferometric tests of general relativity".

4283: 4244: 4197: 4150: 4103: 4056: 4009: 3962: 3900: 3837: 3782: 3720: 3658: 3611: 3564: 3517: 3453: 3392: 3331: 3270: 3165: 3112: 3065: 3008: 2939: 2886: 2833: 2780: 2727: 2674: 2609: 2535: 2481: 2427: 2375: 2141: 2094: 1990: 1765: 1751: 1429: 1408: 1357: 1353: 1224: 702: 2920:

Samuel, Stuart (2003). "On the Speed of Gravity and the v/c Corrections to the Shapiro Time Delay".

1508:(1910). However, those attempts were quickly superseded by Einstein's theory of general relativity. 3434:

Ezquiaga, Jose María & Zumalacárregui, Miguel (16 October 2017). "Dark energy after GW170817".

1659: 1618: 1568: 1365: 1295: 1196: 1065: 897: 877: 867: 862: 847: 614: 169: 50: 3199: 1773: 1710: 757: 4397: 4371: 4350: 4324: 4299: 4273: 4234: 4213: 4187: 4166: 4140: 4119: 4093: 4072: 4046: 4025: 3999: 3978: 3952: 3929: 3916: 3890: 3861: 3827: 3798: 3772: 3749: 3736: 3710: 3687: 3674: 3648: 3627: 3601: 3580: 3554: 3533: 3507: 3477: 3443: 3416: 3382: 3355: 3321: 3294: 3260: 3181: 3155: 3128: 3102: 3055: 3024: 2998: 2963: 2929: 2902: 2876: 2849: 2823: 2796: 2770: 2743: 2717: 2690: 2664: 2599: 2551: 2525: 2497: 2471: 2391: 1980: 1699: 1647: 1581: 1572: 1561: 1538: 1119: 1081: 1077: 1061: 947: 832: 604: 509: 494: 455: 317: 3748:

Faber, Joshua A. (Mar 14, 2003). "The speed of gravity has not been measured from time delays".

3044:"Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A" 4423: 3853: 3469: 3408: 3347: 3286: 2955: 2637: 2354: 2186: 2157: 2027: 1945: 1939: 1743: 1505: 1501: 1451: 1412: 1208: 1132: 827: 777: 552: 214: 104: 2415: 2070: 4454: 4389: 4342: 4291: 4252: 4205: 4158: 4111: 4064: 4017: 3970: 3908: 3845: 3790: 3728: 3666: 3619: 3572: 3525: 3461: 3400: 3339: 3278: 3173: 3120: 3073: 3016: 2947: 2894: 2841: 2788: 2735: 2682: 2627: 2617: 2543: 2489: 2383: 2149: 2137: 1998: 1592: 1361: 1204: 922: 902: 857: 837: 782: 302: 251: 27: 3312:

Creminelli, Paolo & Vernizzi, Filippo (16 October 2017). "Dark energy after GW170817".

1223:

The first attempt to combine a finite gravitational speed with Newton's theory was made by

3873:

Kopeikin, Sergei & Fomalont, Edward (2006). "On the speed of gravity and relativistic

3592:

Will, Clifford M. (2003). "Propagation Speed of Gravity and the Relativistic Time Delay".

2981:

Kopeikin, Sergei & Fomalont, Edward (2006). "On the speed of gravity and relativistic

2265: 2047: 1758: 1735: 1731: 1404: 1298:). Putting the Sun immobile at the origin, when the Earth is moving in an orbit of radius 1278: 1156: 957: 932: 817: 812: 676: 557: 519: 1373: 727: 4393: 4385: 4338: 4287: 4248: 4201: 4154: 4107: 4060: 4013: 3966: 3904: 3841: 3786: 3724: 3662: 3615: 3568: 3521: 3457: 3396: 3335: 3274: 3169: 3124: 3116: 3069: 3012: 2943: 2890: 2837: 2784: 2731: 2678: 2613: 2539: 2485: 2431: 2379: 1994: 1738:

announced that they had measured the speed of gravity indirectly, using their data from

1463:

Henri Poincaré argued in 1904 that a propagation speed of gravity which is greater than

2632: 2587: 2179: 2112: 2023: 1674: 1110: 1089: 1000: 967: 962: 650: 514: 86: 71: 4429: 4068: 4021: 3794: 3732: 2547: 2493: 2310:

Reprinted in Poincaré, Oeuvres, tome IX, S. 551–586 and in "Science and Method" (1908)

2243: 1607:

Aberration of field direction in general relativity, for a weakly accelerated observer

4464: 4401: 4178:

Samuel, Stuart (2004). "On the Speed of Gravity and the Jupiter/Quasar Measurement".

4029: 3802: 3359: 3298: 3185: 2555: 2395: 2101:, Volume IV, Book X, Chapter VII, translated by N. Bowditch (Chelsea, New York, 1966) 1718: 1703: 1651: 1517: 1339:, and the effect preserves energy and angular momentum, so that orbits do not decay. 1310:, moves the Sun's true position ahead of its optical position, by an amount equal to 927: 887: 842: 822: 747: 645: 524: 4354: 4303: 4170: 4076: 3982: 3920: 3865: 3740: 3678: 3631: 3584: 3481: 3420: 3132: 3028: 2967: 2853: 2800: 2747: 2694: 2501: 2416:"Breaking in the 4-vectors: the four-dimensional movement in gravitation, 1905–1910" 2342:. Vol. 1. Boston and New York: Houghton, Mifflin and Company. pp. 604–622. 2335: 2210: 2003: 1966: 1286:

if its position was retarded using the relative velocity (this retardation actually

4447: 4217: 4123: 3928:

Hideki, Asada (Aug 20, 2003). "Comments on "Measuring the Gravity Speed by VLBI"".

3912: 3537: 3465: 3404: 3343: 3177: 3020: 2906: 1769: 1706: 1192: 1140: 872: 852: 3849: 2951: 2320:

Poincaré, Henri (1904). "L'état actuel et l'avenir de la physique mathématique".

1240:

is the speed of gravity. The effect of a finite speed of gravity goes to zero as

2358: 2206: 2153: 1384: 1277:

From a modern point of view, Laplace's analysis is incorrect. Not knowing about

762: 732: 176: 144: 3282: 3078: 3043: 2898: 2845: 2146:

Encyklopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen

1941:

Elementary and Intermediate Algebra: A Combined Course, Student Support Edition

4346: 4295: 4256: 4209: 4162: 4115: 3974: 2792: 972: 534: 460: 229: 150: 3290: 1785: 1663: 543: 285: 3857: 3473: 3412: 3351: 2959: 2641: 2270: 1215:

at a significantly different rate from that predicted by Newtonian theory.

3545:

Asada, Hidecki (2002). "The Light-cone Effect on the Shapiro Time Delay".

4455:

MU physicist defends Einstein's theory and 'speed of gravity' measurement

4192: 3957: 3934: 3832: 3754: 3692: 3653: 3606: 3559: 2934: 2775: 2722: 2669: 1804: 1666: 1152: 1085: 1073: 912: 722: 562: 4084:

Pascual-Sánchez, J.-F. (2004). "Speed of gravity and gravitomagnetism".

2622: 1383:

However, a more important variation of those attempts was the theory of

2387: 1747: 392:{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }} 184: 4278: 4239: 4145: 4131:

Kopeikin, Sergei (2006). "Gravitomagnetism and the speed of gravity".

4098: 4051: 4004: 3895: 3777: 3715: 3512: 3003: 2881: 2828: 2708:

Asada, Hideki (2002). "Light cone effect and the Shapiro time delay".

2604: 2530: 2476: 2445: 1985: 1822:, is constrained to between −3×10 and +7×10 times the speed of light. 1755: 1144: 1069: 240: 221: 202: 115: 1599:. The gravitoelectric field is a static field and therefore cannot 3670: 3623: 3576: 3529: 3448: 3387: 3326: 3265: 3160: 3107: 3060: 2739: 2686: 2340:

Congress of arts and science, universal exposition, St. Louis, 1904

1702:) can be calculated from observations of the orbital decay rate of 4376: 4329: 1255: 1136: 158: 3200:"Quest to settle riddle over Einstein's theory may soon be over" 1739: 195: 2212:"Die räumliche und zeitliche Ausbreitung der Gravitation" 1306:

presuming that the gravitational influence moves with velocity

210: 2588:"The confrontation between general relativity and experiment" 1372:, but they could not provide exact values. One exception was 1376:

in 1890, who succeeded in doing so by combining the laws of

1944:(4th illustrated ed.). Cengage Learning. p. 197. 2462:

Carlip, S. (2000). "Aberration and the Speed of Gravity".

2020:

Gravity: An introduction to Einstein's General Relativity

4362:

Zhu, Yin (2011). "Measurement of the Speed of Gravity".

3810:

Samuel, Stuart (2003). "On the Speed of Gravity and the

2414:

Walter, Scott A. (2007). Renn, J.; Schemmel, M. (eds.).

4321:

A Giant Step: From Milli- to Micro-arcsecond Astrometry

2446:

On the Multiple Deaths of Whitehead's Theory of Gravity

2269: 1673:. The tidal gravitational field is associated with the 3226:"Theoretical battle: Dark energy vs. modified gravity" 2569:

Kopeikin, S.; Efroimsky, M. & Kaplan, G. (2011).

335: 2572:

Relativistic Celestial Mechanics in the Solar System

1754:

across the line-of-sight of the bright radio source

1688:

Relativistic Celestial Mechanics in the Solar System

1471:(based on synchronization by light signals) and the 1167:

The speed of physical changes in a gravitational or

4313:

Proceedings of the International Astronomical Union

2450:

Studies In History And Philosophy Of Modern Physics

1698:The speed of gravity (more correctly, the speed of 300: 283: 265: 249: 238: 227: 208: 193: 182: 167: 156: 142: 130: 125: 114: 103: 85: 70: 49: 44: 26: 21: 2178: 1584:in which the distant charged body is now at rest. 391: 1709:(the Hulse–Taylor binary system noted above) and 2181:Mercury's perihelion, from Leverrier to Einstein 1726:Jovian occultation of QSO J0842+1835 (contested) 45:Approximate values (to three significant digits) 2302:Revue Générale des Sciences Pures et Appliquées 1490: 1477: 1443: 3095:Journal of Cosmology and Astroparticle Physics 2344:Reprinted in "The value of science", Ch. 7–9. 2090: 2088: 1407:tried to explain gravity on the basis of his 1264:for the origin of gravity, the Earth spirals 1236:is the relative speed between the bodies and 1053:Physical constant equal to the speed of light 1034: 8: 4443:article on Kopeikin's original announcement. 2367:Rendiconti del Circolo Matematico di Palermo 1799:GW170817 and the demise of two neutron stars 1591:component of a gravitational field is not a 16: 4437:First speed of gravity measurement revealed 1068:propagate. A change in the distribution of 4416:Does Gravity Travel at the Speed of Light? 2148:(in German). Vol. 5. pp. 25–67. 1938:Larson, Ron; Hostetler, Robert P. (2007). 1041: 1027: 593: 483: 313: 4375: 4328: 4277: 4238: 4191: 4144: 4097: 4050: 4003: 3956: 3933: 3894: 3831: 3776: 3753: 3714: 3691: 3652: 3605: 3558: 3511: 3447: 3386: 3325: 3264: 3159: 3106: 3077: 3059: 3002: 2933: 2880: 2827: 2774: 2721: 2668: 2631: 2621: 2603: 2529: 2475: 2002: 1984: 1967:"The basics of gravitational wave theory" 1595:component (gravitational radiation); see 380: 371: 359: 340: 334: 3881:corrections to the Shapiro time delay". 3818:Corrections to the Shapiro Time Delay". 2989:corrections to the Shapiro time delay". 2336:"The Principles of Mathematical Physics" 1104:The speed of gravitational waves in the 4448:Has the Speed of Gravity Been Measured? 1930: 1850: 1211:determined in 1859 that the elliptical 663: 637: 596: 542: 316: 1516:, light bending, perihelion shift and 1251:mechanical explanations of gravitation 15: 2444:Will, Clifford & Gibbons, Gary. " 2271:"Considerations on Gravitation" 1500:Similar models were also proposed by 1147:that make up light (hence carrier of 126:Approximate light signal travel times 7: 2217:Zeitschrift für Mathematische Physik 1415:. After proposing (and rejecting) a 1084:and confirmed by observation of the 2323:Bulletin des Sciences Mathématiques 2099:"A Treatise in Celestial Mechanics" 1965:Flanagan E.E., Hughes S.A. (2005). 1331:, the effect on the orbit is order 1294:position of the Sun, and is called 4266:General Relativity and Gravitation 3042:Abbott, B.P.; et al. (2017). 1827:alternatives to general relativity 352: 14: 3048:The Astrophysical Journal Letters 2710:The Astrophysical Journal Letters 2420:The Genesis of General Relativity 2113:"Laplace on the Speed of Gravity" 1533:General relativity predicts that 1510:Whitehead's theory of gravitation 1058:classical theories of gravitation 2359:"Sur la dynamique de l'électron" 1467:would contradict the concept of 1008: 1007: 994: 324: 1244:goes to infinity, but not as 1/ 4430:Measuring the Speed of Gravity 3913:10.1016/j.physleta.2006.02.028 3466:10.1103/PhysRevLett.119.251304 3405:10.1103/PhysRevLett.119.251303 3344:10.1103/PhysRevLett.119.251302 3178:10.1016/j.physletb.2016.12.048 3021:10.1016/j.physleta.2006.02.028 2338:. In Rogers, Howard J. (ed.). 1764:Several physicists, including 1750:on its orbit during Jupiter's 1: 4394:10.1088/0256-307X/28/7/070401 3850:10.1103/PhysRevLett.90.231101 3765:Classical and Quantum Gravity 3733:10.1016/S0375-9601(03)00613-3 3125:10.1088/1475-7516/2016/03/031 2952:10.1103/PhysRevLett.90.231101 2494:10.1016/S0375-9601(00)00101-8 1425:Johann Karl Friedrich Zöllner 1370:perihelion advance of Mercury 1135:. Such particles include the 266:from the nearest galaxy (the 2592:Living Reviews in Relativity 2295:"La dynamique de l'électron" 2185:. Oxford: University Press. 1669:symbolize the gravitational 1106:general theory of relativity 1086:GW170817 neutron star merger 4069:10.1088/0264-9381/22/23/N01 4022:10.1088/0264-9381/21/15/011 3795:10.1088/0264-9381/21/13/010 2548:10.1088/0264-9381/21/15/011 2154:10.1007/978-3-663-16016-8_2 2058:(2nd ed.). p. 12. 1421:Ottaviano-Fabrizio Mossotti 505:Gravitational time dilation 4492: 3283:10.1103/PhysRevD.95.084029 2899:10.1103/PhysRevD.65.064025 2846:10.1103/PhysRevD.60.124002 1624:Liénard–Wiechert potential 1613:Liénard–Wiechert potential 1610: 1587:The static and continuous 1567:A moving body's seeing no 1343:Electrodynamical analogies 1213:orbit of Mercury precesses 625:Mathisson–Papapetrou–Dixon 466:Pseudo-Riemannian manifold 4347:10.1017/S1743921308019613 4296:10.1007/s10714-007-0483-6 4257:10.1142/S021827180600853X 4210:10.1142/S0218271804005900 4163:10.1142/S0218271806007663 4116:10.1142/S0218271804006425 3975:10.1007/s10701-006-9059-7 2793:10.1007/s10701-006-9059-7 2657:The Astrophysical Journal 2332:. English translation in 2004:10.1088/1367-2630/7/1/204 1694:PSR 1913+16 orbital decay 1428:in which it was shown by 1262:a Fatio/Le Sage mechanism 1080:, which, as predicted by 3079:10.3847/2041-8213/aa920c 2334:Poincaré, Henri (1905). 2177:Roseveare, N. T (1982). 1829:, including variants of 1825:This also excluded some 1730:In September 2002, 1632:electromagnetic emission 1459:Lorentz covariant models 1151:), and the hypothetical 630:Hamilton–Jacobi–Einstein 610:Einstein field equations 433:Mathematical formulation 268:Canis Major Dwarf Galaxy 4364:Chinese Physics Letters 3436:Physical Review Letters 3375:Physical Review Letters 3314:Physical Review Letters 2922:Physical Review Letters 2822:(12): id. 124002. 2052:Wheeler, John Archibald 1839:Hořava–Lifshitz gravity 1656:gravitational potential 1554:gravitoelectromagnetism 1535:gravitational radiation 1514:gravitational red shift 1473:principle of relativity 1296:annual solar aberration 1118:. Within the theory of 3945:Foundations of Physics 3148:Physics Letters B 2875:(6): id. 064025. 2869:Physical Review D 2816:Physical Review D 2763:Foundations of Physics 2448:", to be submitted to 2069:Verrier U. Le (1859). 1972:New Journal of Physics 1498: 1486:Lorentz transformation 1482: 1448: 1274: 500:Gravitational redshift 393: 183:the length of Earth's 2293:Poincaré, H. (1908). 2276:Proc. Acad. Amsterdam 2018:Hartle, J.B. (2003). 1715:gravitational damping 1642:Formulaic conventions 1597:Petrov classification 1259: 1201:Newtonian gravitation 1188:Newtonian gravitation 1169:electromagnetic field 1149:electromagnetic force 788:Weyl−Lewis−Papapetrou 743:Kerr–Newman–de Sitter 563:Einstein–Rosen bridge 495:Gravitational lensing 451:Equivalence principle 394: 4227:Int. J. Mod. Phys. D 4180:Int. J. Mod. Phys. D 4133:Int. J. Mod. Phys. D 4086:Int. J. Mod. Phys. D 2026:. pp. 332–333. 1831:scalar–tensor theory 1722:cannot be infinite. 1430:Pierre-Simon Laplace 1358:Carl Friedrich Gauss 1354:Wilhelm Eduard Weber 1203:is described by the 1195:'s formulation of a 718:Einstein–Rosen waves 444:Fundamental concepts 333: 4386:2011ChPhL..28g0401Z 4339:2008IAUS..248..383F 4288:2007GReGr..39.1583K 4249:2006IJMPD..15..273K 4202:2004IJMPD..13.1753S 4155:2006IJMPD..15..305K 4108:2004IJMPD..13.2345P 4061:2005CQGra..22.5181K 4039:Class. Quantum Grav 4014:2004CQGra..21.3803C 3992:Class. Quantum Grav 3967:2006FoPh...36.1244K 3905:2006PhLA..355..163K 3842:2003PhRvL..90w1101S 3787:2004CQGra..21.3251K 3725:2003PhLA..312..147K 3663:2003ApJ...598..704F 3616:2003ApJ...590..683W 3569:2002ApJ...574L..69A 3522:2001ApJ...556L...1K 3458:2017PhRvL.119y1304E 3397:2017PhRvL.119y1303S 3336:2017PhRvL.119y1302C 3275:2017PhRvD..95h4029B 3170:2017PhLB..765..382L 3117:2016JCAP...03..031L 3070:2017ApJ...848L..13A 3013:2006PhLA..355..163K 2944:2003PhRvL..90w1101S 2891:2002PhRvD..65f4025K 2838:1999PhRvD..60l4002K 2785:2006FoPh...36.1244K 2732:2002ApJ...574L..69A 2679:2003ApJ...598..704F 2623:10.12942/lrr-2001-4 2614:2001LRR.....4....4W 2540:2004CQGra..21.3803C 2518:Class. Quantum Grav 2486:2000PhLA..267...81C 2432:2007ggr..conf..193W 2426:. Berlin: 193–252. 2402:English Translation 2380:1906RCMP...21..129P 1995:2005NJPh....7..204F 1742:measurement of the 1700:gravitational waves 1660:Christoffel symbols 1547:Hulse–Taylor binary 1494:ceteris non mutatis 1366:James Clerk Maxwell 1197:gravitational force 1088:, is equal to the 1066:gravitational field 672:Kaluza–Klein theory 558:Minkowski spacetime 510:Gravitational waves 170:geostationary orbit 51:kilometres per hour 18: 4476:History of physics 4471:Effects of gravity 4446:Clifford M. Will, 3232:. 25 February 2017 3206:. 10 February 2017 2388:10.1007/BF03013466 2244:"Gerber's Gravity" 2233:Zenneck, pp. 49–51 1835:Horndeski's theory 1648:general relativity 1576:relative to them. 1562:Lorentz invariance 1539:general relativity 1524:General relativity 1419:, he assumed like 1417:Le Sage type model 1275: 1120:special relativity 1082:general relativity 1078:gravitational wave 1001:Physics portal 773:Oppenheimer–Snyder 713:Reissner–Nordström 605:Linearized gravity 553:Spacetime diagrams 456:Special relativity 389: 318:General relativity 105:astronomical units 4272:(10): 1583–1624. 4092:(10): 2345–2350. 4045:(23): 5181–5186. 3998:(15): 3803–3812. 3883:Physics Letters A 3771:(13): 3251–3286. 3253:Physical Review D 3230:arstechnica.co.uk 2991:Physics Letters A 2586:Will, C. (2001). 2524:(15): 3803–3812. 2192:978-0-19-858174-1 2163:978-3-663-15445-7 2056:Spacetime Physics 2033:978-0-8053-8662-2 2022:. San Francisco: 1951:978-0-618-75354-3 1869:× 60 × 60 × 24 / 1803:The detection of 1744:retarded position 1506:Arnold Sommerfeld 1502:Hermann Minkowski 1413:Maxwell equations 1323:almost infinite. 1209:Urbain Le Verrier 1133:massless particle 1051: 1050: 684: 683: 570: 569: 312: 311: 308:2.5 million years 28:metres per second 4483: 4405: 4379: 4358: 4332: 4307: 4281: 4260: 4242: 4221: 4195: 4193:astro-ph/0412401 4186:(9): 1753–1770. 4174: 4148: 4127: 4101: 4080: 4054: 4033: 4007: 3986: 3960: 3958:astro-ph/0311063 3951:(8): 1244–1285. 3939: 3937: 3935:astro-ph/0308343 3924: 3898: 3869: 3835: 3833:astro-ph/0304006 3806: 3780: 3759: 3757: 3755:astro-ph/0303346 3744: 3718: 3709:(3–4): 147–157. 3697: 3695: 3693:astro-ph/0302462 3682: 3656: 3654:astro-ph/0302294 3635: 3609: 3607:astro-ph/0301145 3588: 3562: 3560:astro-ph/0206266 3541: 3515: 3486: 3485: 3451: 3431: 3425: 3424: 3390: 3370: 3364: 3363: 3329: 3309: 3303: 3302: 3268: 3248: 3242: 3241: 3239: 3237: 3222: 3216: 3215: 3213: 3211: 3196: 3190: 3189: 3163: 3143: 3137: 3136: 3110: 3090: 3084: 3083: 3081: 3063: 3039: 3033: 3032: 3006: 2978: 2972: 2971: 2937: 2935:astro-ph/0304006 2917: 2911: 2910: 2884: 2864: 2858: 2857: 2831: 2811: 2805: 2804: 2778: 2776:astro-ph/0311063 2769:(8): 1244–1285. 2758: 2752: 2751: 2725: 2723:astro-ph/0206266 2705: 2699: 2698: 2672: 2670:astro-ph/0302294 2652: 2646: 2645: 2635: 2625: 2607: 2583: 2577: 2576: 2566: 2560: 2559: 2533: 2512: 2506: 2505: 2479: 2459: 2453: 2442: 2436: 2435: 2411: 2405: 2399: 2363: 2351: 2345: 2343: 2331: 2317: 2311: 2309: 2299: 2290: 2284: 2283: 2273: 2262: 2256: 2255: 2253: 2251: 2240: 2234: 2231: 2225: 2224: 2214: 2203: 2197: 2196: 2184: 2174: 2168: 2167: 2134: 2128: 2127: 2125: 2123: 2111:Brown, Kevin S. 2108: 2102: 2092: 2083: 2082: 2066: 2060: 2059: 2048:Taylor, Edwin F. 2044: 2038: 2037: 2015: 2009: 2008: 2006: 1988: 1962: 1956: 1955: 1935: 1919: 1918: 1916: 1915: 1912: 1909: 1903: 1902: 1899: 1890: 1884: 1883: 1881: 1880: 1877: 1874: 1868: 1867: 1864: 1855: 1818: 1811: 1766:Clifford M. Will 1512:(1922) explains 1394: 1392: 1362:Bernhard Riemann 1290:happen with the 1273:towards the Sun. 1205:Poisson equation 1139:(carrier of the 1129: 1125: 1117: 1108:is equal to the 1043: 1036: 1029: 1016: 1011: 1010: 1003: 999: 998: 783:van Stockum dust 768:Robertson–Walker 594: 484: 398: 396: 395: 390: 388: 387: 375: 367: 366: 348: 347: 328: 314: 303:Andromeda Galaxy 296: 294: 279: 277: 257: 99: 98: 95: 81: 80: 72:miles per second 66: 65: 62: 59: 40: 39: 36: 19: 17:Speed of gravity 4491: 4490: 4486: 4485: 4484: 4482: 4481: 4480: 4461: 4460: 4453:Kevin Carlson, 4420:The Physics FAQ 4412: 4361: 4310: 4263: 4224: 4177: 4130: 4083: 4036: 3989: 3942: 3927: 3872: 3820:Phys. Rev. Lett 3809: 3762: 3747: 3700: 3685: 3638: 3591: 3544: 3497: 3494: 3492:Further reading 3489: 3433: 3432: 3428: 3372: 3371: 3367: 3311: 3310: 3306: 3250: 3249: 3245: 3235: 3233: 3224: 3223: 3219: 3209: 3207: 3198: 3197: 3193: 3145: 3144: 3140: 3092: 3091: 3087: 3041: 3040: 3036: 2980: 2979: 2975: 2919: 2918: 2914: 2866: 2865: 2861: 2813: 2812: 2808: 2760: 2759: 2755: 2707: 2706: 2702: 2654: 2653: 2649: 2585: 2584: 2580: 2568: 2567: 2563: 2515: 2513: 2509: 2461: 2460: 2456: 2443: 2439: 2413: 2412: 2408: 2361: 2353: 2352: 2348: 2333: 2319: 2318: 2314: 2297: 2292: 2291: 2287: 2264: 2263: 2259: 2249: 2247: 2242: 2241: 2237: 2232: 2228: 2205: 2204: 2200: 2193: 2176: 2175: 2171: 2164: 2136: 2135: 2131: 2121: 2119: 2110: 2109: 2105: 2093: 2086: 2075:C. R. Acad. Sci 2068: 2067: 2063: 2046: 2045: 2041: 2034: 2017: 2016: 2012: 1964: 1963: 1959: 1952: 1937: 1936: 1932: 1928: 1923: 1922: 1913: 1910: 1907: 1905: 1900: 1897: 1895: 1893: 1891: 1887: 1878: 1875: 1872: 1870: 1865: 1862: 1860: 1858: 1856: 1852: 1847: 1833:, instances of 1821: 1816: 1814: 1809: 1801: 1736:Edward Fomalont 1732:Sergei Kopeikin 1728: 1696: 1683: 1654:symbolizes the 1644: 1615: 1609: 1593:gravitomagnetic 1589:gravitoelectric 1582:reference frame 1573:reference frame 1531: 1526: 1461: 1405:Hendrik Lorentz 1401: 1390: 1388: 1350: 1345: 1221: 1190: 1165: 1157:quantum gravity 1127: 1123: 1122:, the constant 1115: 1102: 1054: 1047: 1006: 993: 992: 985: 984: 808: 807: 798: 797: 753:Lemaître–Tolman 698: 697: 686: 685: 677:Quantum gravity 664:Advanced theory 591: 590: 589: 572: 571: 520:Geodetic effect 481: 480: 471: 470: 446: 445: 429: 399: 376: 355: 336: 331: 330: 292: 290: 275: 273: 255: 96: 93: 91: 78: 76: 63: 60: 57: 55: 37: 34: 32: 12: 11: 5: 4489: 4487: 4479: 4478: 4473: 4463: 4462: 4459: 4458: 4451: 4444: 4433: 4427: 4411: 4410:External links 4408: 4407: 4406: 4359: 4308: 4261: 4233:(2): 273–288. 4222: 4175: 4139:(3): 305–320. 4128: 4081: 4034: 3987: 3940: 3925: 3889:(3): 163–166. 3870: 3826:(23): 231101. 3807: 3760: 3745: 3698: 3683: 3671:10.1086/378785 3647:(1): 704–711. 3636: 3624:10.1086/375164 3600:(2): 683–690. 3589: 3577:10.1086/342369 3553:(1): L69–L70. 3542: 3530:10.1086/322872 3493: 3490: 3488: 3487: 3442:(25): 251304. 3426: 3381:(25): 251303. 3365: 3320:(25): 251302. 3304: 3243: 3217: 3191: 3138: 3085: 3034: 2997:(3): 163–166. 2973: 2928:(23): 231101. 2912: 2859: 2806: 2753: 2740:10.1086/342369 2716:(1): L69–L70. 2700: 2687:10.1086/378785 2663:(1): 704–711. 2647: 2578: 2561: 2507: 2470:(2–3): 81–87. 2454: 2437: 2406: 2374:(1): 129–176. 2346: 2312: 2285: 2257: 2235: 2226: 2198: 2191: 2169: 2162: 2129: 2103: 2084: 2061: 2039: 2032: 2024:Addison-Wesley 2010: 1957: 1950: 1929: 1927: 1924: 1921: 1920: 1885: 1849: 1848: 1846: 1843: 1819: 1812: 1800: 1797: 1759:QSO J0842+1835 1727: 1724: 1704:binary pulsars 1695: 1692: 1682: 1679: 1677:of spacetime. 1643: 1640: 1611:Main article: 1608: 1605: 1601:superluminally 1530: 1527: 1525: 1522: 1460: 1457: 1452:Henri Poincaré 1400: 1397: 1349: 1348:Early theories 1346: 1344: 1341: 1302:with velocity 1220: 1217: 1189: 1186: 1164: 1161: 1111:speed of light 1101: 1098: 1090:speed of light 1052: 1049: 1048: 1046: 1045: 1038: 1031: 1023: 1020: 1019: 1018: 1017: 1004: 987: 986: 983: 982: 975: 970: 965: 960: 955: 950: 945: 940: 935: 930: 925: 920: 915: 910: 905: 900: 895: 890: 885: 880: 875: 870: 865: 860: 855: 850: 845: 840: 835: 830: 825: 820: 815: 809: 805: 804: 803: 800: 799: 796: 795: 790: 785: 780: 775: 770: 765: 760: 755: 750: 745: 740: 735: 730: 725: 720: 715: 710: 699: 693: 692: 691: 688: 687: 682: 681: 680: 679: 674: 666: 665: 661: 660: 659: 658: 656:Post-Newtonian 653: 648: 640: 639: 635: 634: 633: 632: 627: 622: 617: 612: 607: 599: 598: 592: 588: 587: 584: 580: 579: 578: 577: 574: 573: 568: 567: 566: 565: 560: 555: 547: 546: 540: 539: 538: 537: 532: 527: 522: 517: 515:Frame-dragging 512: 507: 502: 497: 492: 490:Kepler problem 482: 478: 477: 476: 473: 472: 469: 468: 463: 458: 453: 447: 443: 442: 441: 438: 437: 436: 435: 430: 428: 427: 422: 417: 411: 409: 401: 400: 386: 383: 379: 374: 370: 365: 362: 358: 354: 351: 346: 343: 339: 329: 321: 320: 310: 309: 306: 298: 297: 288: 281: 280: 271: 263: 262: 259: 247: 246: 243: 236: 235: 232: 225: 224: 218: 206: 205: 199: 191: 190: 187: 180: 179: 173: 165: 164: 161: 154: 153: 147: 140: 139: 134: 128: 127: 123: 122: 119: 112: 111: 108: 101: 100: 89: 87:miles per hour 83: 82: 74: 68: 67: 53: 47: 46: 42: 41: 30: 24: 23: 13: 10: 9: 6: 4: 3: 2: 4488: 4477: 4474: 4472: 4469: 4468: 4466: 4456: 4452: 4449: 4445: 4442: 4441:New Scientist 4438: 4434: 4431: 4428: 4425: 4421: 4417: 4414: 4413: 4409: 4403: 4399: 4395: 4391: 4387: 4383: 4378: 4373: 4370:(7): 070401. 4369: 4365: 4360: 4356: 4352: 4348: 4344: 4340: 4336: 4331: 4326: 4322: 4318: 4314: 4309: 4305: 4301: 4297: 4293: 4289: 4285: 4280: 4279:gr-qc/0510077 4275: 4271: 4267: 4262: 4258: 4254: 4250: 4246: 4241: 4240:gr-qc/0501001 4236: 4232: 4228: 4223: 4219: 4215: 4211: 4207: 4203: 4199: 4194: 4189: 4185: 4181: 4176: 4172: 4168: 4164: 4160: 4156: 4152: 4147: 4146:gr-qc/0507001 4142: 4138: 4134: 4129: 4125: 4121: 4117: 4113: 4109: 4105: 4100: 4099:gr-qc/0405123 4095: 4091: 4087: 4082: 4078: 4074: 4070: 4066: 4062: 4058: 4053: 4052:gr-qc/0510048 4048: 4044: 4040: 4035: 4031: 4027: 4023: 4019: 4015: 4011: 4006: 4005:gr-qc/0403060 4001: 3997: 3993: 3988: 3984: 3980: 3976: 3972: 3968: 3964: 3959: 3954: 3950: 3946: 3941: 3936: 3931: 3926: 3922: 3918: 3914: 3910: 3906: 3902: 3897: 3896:gr-qc/0310065 3892: 3888: 3884: 3880: 3876: 3871: 3867: 3863: 3859: 3855: 3851: 3847: 3843: 3839: 3834: 3829: 3825: 3821: 3817: 3813: 3808: 3804: 3800: 3796: 3792: 3788: 3784: 3779: 3778:gr-qc/0310059 3774: 3770: 3766: 3761: 3756: 3751: 3746: 3742: 3738: 3734: 3730: 3726: 3722: 3717: 3716:gr-qc/0212121 3712: 3708: 3704: 3703:Phys. Lett. A 3699: 3694: 3689: 3684: 3680: 3676: 3672: 3668: 3664: 3660: 3655: 3650: 3646: 3642: 3637: 3633: 3629: 3625: 3621: 3617: 3613: 3608: 3603: 3599: 3595: 3590: 3586: 3582: 3578: 3574: 3570: 3566: 3561: 3556: 3552: 3548: 3543: 3539: 3535: 3531: 3527: 3523: 3519: 3514: 3513:gr-qc/0105060 3509: 3505: 3501: 3496: 3495: 3491: 3483: 3479: 3475: 3471: 3467: 3463: 3459: 3455: 3450: 3445: 3441: 3437: 3430: 3427: 3422: 3418: 3414: 3410: 3406: 3402: 3398: 3394: 3389: 3384: 3380: 3376: 3369: 3366: 3361: 3357: 3353: 3349: 3345: 3341: 3337: 3333: 3328: 3323: 3319: 3315: 3308: 3305: 3300: 3296: 3292: 3288: 3284: 3280: 3276: 3272: 3267: 3262: 3259:(8): 084029. 3258: 3254: 3247: 3244: 3231: 3227: 3221: 3218: 3205: 3201: 3195: 3192: 3187: 3183: 3179: 3175: 3171: 3167: 3162: 3157: 3153: 3149: 3142: 3139: 3134: 3130: 3126: 3122: 3118: 3114: 3109: 3104: 3100: 3096: 3089: 3086: 3080: 3075: 3071: 3067: 3062: 3057: 3053: 3049: 3045: 3038: 3035: 3030: 3026: 3022: 3018: 3014: 3010: 3005: 3004:gr-qc/0310065 3000: 2996: 2992: 2988: 2984: 2977: 2974: 2969: 2965: 2961: 2957: 2953: 2949: 2945: 2941: 2936: 2931: 2927: 2923: 2916: 2913: 2908: 2904: 2900: 2896: 2892: 2888: 2883: 2882:gr-qc/0110101 2878: 2874: 2870: 2863: 2860: 2855: 2851: 2847: 2843: 2839: 2835: 2830: 2829:gr-qc/9902030 2825: 2821: 2817: 2810: 2807: 2802: 2798: 2794: 2790: 2786: 2782: 2777: 2772: 2768: 2764: 2757: 2754: 2749: 2745: 2741: 2737: 2733: 2729: 2724: 2719: 2715: 2711: 2704: 2701: 2696: 2692: 2688: 2684: 2680: 2676: 2671: 2666: 2662: 2658: 2651: 2648: 2643: 2639: 2634: 2629: 2624: 2619: 2615: 2611: 2606: 2605:gr-qc/0103036 2601: 2597: 2593: 2589: 2582: 2579: 2574: 2573: 2565: 2562: 2557: 2553: 2549: 2545: 2541: 2537: 2532: 2531:gr-qc/0403060 2527: 2523: 2519: 2511: 2508: 2503: 2499: 2495: 2491: 2487: 2483: 2478: 2477:gr-qc/9909087 2473: 2469: 2465: 2464:Phys. Lett. A 2458: 2455: 2451: 2447: 2441: 2438: 2433: 2429: 2425: 2421: 2417: 2410: 2407: 2403: 2400:See also the 2397: 2393: 2389: 2385: 2381: 2377: 2373: 2370:(in French). 2369: 2368: 2360: 2356: 2350: 2347: 2341: 2337: 2330:(2): 302–324. 2329: 2325: 2324: 2316: 2313: 2307: 2303: 2296: 2289: 2286: 2281: 2277: 2272: 2267: 2266:Lorentz, H.A. 2261: 2258: 2245: 2239: 2236: 2230: 2227: 2222: 2219:(in German). 2218: 2213: 2208: 2202: 2199: 2194: 2188: 2183: 2182: 2173: 2170: 2165: 2159: 2155: 2151: 2147: 2143: 2142:"Gravitation" 2139: 2133: 2130: 2118: 2114: 2107: 2104: 2100: 2096: 2095:Laplace, P.S. 2091: 2089: 2085: 2080: 2076: 2072: 2065: 2062: 2057: 2053: 2049: 2043: 2040: 2035: 2029: 2025: 2021: 2014: 2011: 2005: 2000: 1996: 1992: 1987: 1986:gr-qc/0501041 1982: 1978: 1974: 1973: 1968: 1961: 1958: 1953: 1947: 1943: 1942: 1934: 1931: 1925: 1892:Exact value: 1889: 1886: 1857:Exact value: 1854: 1851: 1844: 1842: 1840: 1836: 1832: 1828: 1823: 1806: 1798: 1796: 1794: 1793:Stuart Samuel 1790: 1787: 1781: 1777: 1775: 1771: 1767: 1762: 1760: 1757: 1753: 1749: 1745: 1741: 1737: 1733: 1725: 1723: 1720: 1719:PPN formalism 1716: 1712: 1708: 1705: 1701: 1693: 1691: 1689: 1680: 1678: 1676: 1672: 1668: 1665: 1661: 1657: 1653: 1652:metric tensor 1649: 1641: 1639: 1635: 1633: 1629: 1625: 1620: 1614: 1606: 1604: 1602: 1598: 1594: 1590: 1585: 1583: 1577: 1574: 1570: 1565: 1563: 1557: 1555: 1550: 1548: 1542: 1540: 1536: 1528: 1523: 1521: 1519: 1518:Shapiro delay 1515: 1511: 1507: 1503: 1497: 1495: 1489: 1487: 1481: 1476: 1474: 1470: 1466: 1458: 1456: 1453: 1447: 1442: 1440: 1436: 1431: 1426: 1422: 1418: 1414: 1410: 1406: 1398: 1396: 1386: 1381: 1379: 1375: 1371: 1367: 1363: 1359: 1355: 1347: 1342: 1340: 1338: 1334: 1330: 1324: 1321: 1317: 1313: 1309: 1305: 1301: 1297: 1293: 1289: 1285: 1280: 1272: 1267: 1263: 1258: 1254: 1252: 1247: 1243: 1239: 1235: 1231: 1226: 1218: 1216: 1214: 1210: 1206: 1202: 1198: 1194: 1187: 1185: 1181: 1177: 1175: 1170: 1163:Static fields 1162: 1160: 1158: 1154: 1150: 1146: 1142: 1138: 1134: 1121: 1114:in a vacuum, 1113: 1112: 1107: 1099: 1097: 1095: 1091: 1087: 1083: 1079: 1075: 1071: 1067: 1063: 1059: 1044: 1039: 1037: 1032: 1030: 1025: 1024: 1022: 1021: 1015: 1005: 1002: 997: 991: 990: 989: 988: 981: 980: 976: 974: 971: 969: 966: 964: 961: 959: 956: 954: 951: 949: 946: 944: 941: 939: 936: 934: 931: 929: 926: 924: 921: 919: 918:Chandrasekhar 916: 914: 911: 909: 906: 904: 901: 899: 896: 894: 891: 889: 886: 884: 881: 879: 876: 874: 871: 869: 866: 864: 861: 859: 856: 854: 851: 849: 846: 844: 841: 839: 836: 834: 833:Schwarzschild 831: 829: 826: 824: 821: 819: 816: 814: 811: 810: 802: 801: 794: 793:Hartle–Thorne 791: 789: 786: 784: 781: 779: 776: 774: 771: 769: 766: 764: 761: 759: 756: 754: 751: 749: 746: 744: 741: 739: 736: 734: 731: 729: 726: 724: 721: 719: 716: 714: 711: 708: 704: 703:Schwarzschild 701: 700: 696: 690: 689: 678: 675: 673: 670: 669: 668: 667: 662: 657: 654: 652: 649: 647: 644: 643: 642: 641: 636: 631: 628: 626: 623: 621: 618: 616: 613: 611: 608: 606: 603: 602: 601: 600: 595: 585: 582: 581: 576: 575: 564: 561: 559: 556: 554: 551: 550: 549: 548: 545: 541: 536: 533: 531: 528: 526: 525:Event horizon 523: 521: 518: 516: 513: 511: 508: 506: 503: 501: 498: 496: 493: 491: 488: 487: 486: 485: 475: 474: 467: 464: 462: 459: 457: 454: 452: 449: 448: 440: 439: 434: 431: 426: 423: 421: 418: 416: 413: 412: 410: 408: 405: 404: 403: 402: 384: 381: 377: 372: 368: 363: 360: 356: 349: 344: 341: 337: 327: 323: 322: 319: 315: 307: 304: 299: 289: 287: 282: 272: 269: 264: 260: 253: 248: 244: 242: 237: 233: 231: 226: 223: 219: 216: 212: 207: 204: 200: 197: 192: 188: 186: 181: 178: 174: 171: 166: 162: 160: 155: 152: 148: 146: 141: 138: 135: 133: 129: 124: 120: 117: 113: 109: 106: 102: 90: 88: 84: 75: 73: 69: 54: 52: 48: 43: 31: 29: 25: 20: 4440: 4435:Hazel Muir, 4432:at MathPages 4419: 4367: 4363: 4323:): 383–386. 4320: 4316: 4312: 4269: 4265: 4230: 4226: 4183: 4179: 4136: 4132: 4089: 4085: 4042: 4038: 3995: 3991: 3948: 3944: 3886: 3882: 3878: 3874: 3823: 3819: 3815: 3811: 3768: 3764: 3706: 3702: 3644: 3641:Astrophys. J 3640: 3597: 3594:Astrophys. J 3593: 3550: 3547:Astrophys. J 3546: 3506:(1): L1–L6. 3503: 3500:Astrophys. J 3499: 3439: 3435: 3429: 3378: 3374: 3368: 3317: 3313: 3307: 3256: 3252: 3246: 3234:. Retrieved 3229: 3220: 3208:. Retrieved 3203: 3194: 3151: 3147: 3141: 3098: 3094: 3088: 3051: 3047: 3037: 2994: 2990: 2986: 2982: 2976: 2925: 2921: 2915: 2872: 2868: 2862: 2819: 2815: 2809: 2766: 2762: 2756: 2713: 2709: 2703: 2660: 2656: 2650: 2595: 2591: 2581: 2575:. Wiley-VCH. 2571: 2564: 2521: 2517: 2510: 2467: 2463: 2457: 2449: 2440: 2423: 2419: 2409: 2371: 2365: 2355:Poincaré, H. 2349: 2339: 2327: 2321: 2315: 2305: 2301: 2288: 2279: 2275: 2260: 2248:. Retrieved 2238: 2229: 2220: 2216: 2201: 2180: 2172: 2145: 2132: 2120:. Retrieved 2116: 2106: 2098: 2078: 2074: 2064: 2055: 2042: 2019: 2013: 1976: 1970: 1960: 1940: 1933: 1888: 1853: 1824: 1802: 1791: 1782: 1778: 1774:Hideki Asada 1770:Steve Carlip 1763: 1729: 1711:PSR B1534+12 1697: 1687: 1684: 1681:Measurements 1645: 1636: 1631: 1628:acceleration 1627: 1616: 1586: 1578: 1566: 1558: 1551: 1543: 1532: 1499: 1493: 1491: 1488:. He wrote: 1483: 1478: 1475:. He wrote: 1464: 1462: 1449: 1444: 1438: 1434: 1409:ether theory 1402: 1382: 1374:Maurice Lévy 1351: 1336: 1332: 1328: 1325: 1319: 1315: 1311: 1307: 1303: 1299: 1291: 1287: 1283: 1276: 1270: 1265: 1245: 1241: 1237: 1233: 1229: 1222: 1193:Isaac Newton 1191: 1182: 1178: 1173: 1166: 1141:strong force 1109: 1103: 1100:Introduction 1093: 1055: 978: 938:Raychaudhuri 407:Introduction 252:nearest star 213:to Earth (1 136: 131: 22:Exact values 3210:10 February 3154:: 382–385. 2246:. Mathpages 2138:Zenneck, J. 1707:PSR 1913+16 1671:force field 1504:(1907) and 1385:Paul Gerber 953:van Stockum 883:Oppenheimer 738:Kerr–Newman 530:Singularity 295: years 284:across the 278: years 4465:Categories 3449:1710.05901 3388:1710.05893 3327:1710.05877 3266:1608.01982 3236:27 October 3161:1602.07670 3108:1509.08458 3101:(3): 031. 3061:1710.05834 3054:(2): L13. 2308:: 386–402. 2282:: 559–574. 2207:Gerber, P. 2081:: 379–383. 1979:(1): 204. 1926:References 1619:aberration 1569:aberration 1529:Background 1469:local time 1393: km/s 806:Scientists 638:Formalisms 586:Formalisms 535:Black hole 461:World line 270:) to Earth 245:3.26 years 230:light year 4402:250811249 4377:1108.3761 4330:0912.4038 4030:250863503 3803:250893542 3360:206304918 3299:119186001 3291:2470-0010 3186:118486016 2556:250863503 2396:120211823 2223:: 93–104. 2117:MathPages 2097:: (1805) 1786:null cone 1675:curvature 1664:spacetime 1450:In 1908, 1403:In 1900, 1153:gravitons 898:Robertson 863:Friedmann 858:Eddington 848:Nordström 838:de Sitter 695:Solutions 620:Geodesics 615:Friedmann 597:Equations 583:Equations 544:Spacetime 479:Phenomena 385:ν 382:μ 373:κ 364:ν 361:μ 353:Λ 345:ν 342:μ 301:from the 286:Milky Way 261:4.2 years 4355:53363773 4304:15412146 4171:18790529 4077:17222421 3983:53514468 3921:12121566 3866:15905017 3858:12857246 3741:11664954 3679:14002701 3632:16402202 3585:14589086 3482:38618360 3474:29303304 3421:39068360 3413:29303345 3352:29303308 3204:phys.org 3133:73517974 3029:12121566 2968:15905017 2960:12857246 2854:53640560 2801:53514468 2748:14589086 2695:14002701 2642:28163632 2598:(1): 4. 2502:12941280 2357:(1906). 2268:(1900). 2209:(1898). 2140:(1903). 2054:(1991). 1882:) AU/day 1805:GW170817 1667:manifold 1411:and the 1284:had been 1266:outwards 1232:, where 1074:momentum 1014:Category 878:Lemaître 843:Reissner 828:Poincaré 813:Einstein 758:Taub–NUT 723:Wormhole 707:interior 420:Timeline 305:to Earth 254:to Sun ( 234:1.0 year 198:to Earth 172:to Earth 132:Distance 118:per year 4382:Bibcode 4335:Bibcode 4319:(S248, 4284:Bibcode 4245:Bibcode 4218:2908984 4198:Bibcode 4151:Bibcode 4124:2402650 4104:Bibcode 4057:Bibcode 4010:Bibcode 3963:Bibcode 3901:Bibcode 3838:Bibcode 3783:Bibcode 3721:Bibcode 3659:Bibcode 3612:Bibcode 3565:Bibcode 3538:2121856 3518:Bibcode 3454:Bibcode 3393:Bibcode 3332:Bibcode 3271:Bibcode 3166:Bibcode 3113:Bibcode 3066:Bibcode 3009:Bibcode 2940:Bibcode 2907:9505866 2887:Bibcode 2834:Bibcode 2781:Bibcode 2728:Bibcode 2675:Bibcode 2633:5253802 2610:Bibcode 2536:Bibcode 2482:Bibcode 2452:(2006). 2428:Bibcode 2376:Bibcode 1991:Bibcode 1752:transit 1748:Jupiter 1662:of the 1399:Lorentz 1292:optical 1279:Lorentz 1271:inwards 1225:Laplace 1219:Laplace 1145:photons 1143:), the 1062:changes 933:Hawking 928:Penrose 903:Bardeen 893:Wheeler 823:Hilbert 818:Lorentz 778:pp-wave 415:History 185:equator 116:parsecs 107:per day 4422:(also 4400: 4353: 4302: 4216: 4169: 4122: 4075: 4028: 3981: 3919: 3864: 3856: 3801: 3739: 3677: 3630: 3583: 3536: 3480: 3472: 3419: 3411: 3358: 3350: 3297: 3289: 3184: 3131: 3027: 2966: 2958: 2905: 2852: 2799: 2746: 2693: 2640: 2630: 2554: 2500: 2394: 2189: 2160: 2030: 1948: 1917:) pc/y 1837:, and 1756:quasar 1658:, and 1446:light. 1070:energy 1060:, the 1012: 979:others 973:Thorne 963:Newman 943:Taylor 923:Ehlers 908:Walker 873:Zwicky 748:Kasner 256:1.3 pc 241:parsec 189:134 ms 163:3.3 ns 4398:S2CID 4372:arXiv 4351:S2CID 4325:arXiv 4300:S2CID 4274:arXiv 4235:arXiv 4214:S2CID 4188:arXiv 4167:S2CID 4141:arXiv 4120:S2CID 4094:arXiv 4073:S2CID 4047:arXiv 4026:S2CID 4000:arXiv 3979:S2CID 3953:arXiv 3930:arXiv 3917:S2CID 3891:arXiv 3862:S2CID 3828:arXiv 3799:S2CID 3773:arXiv 3750:arXiv 3737:S2CID 3711:arXiv 3688:arXiv 3675:S2CID 3649:arXiv 3628:S2CID 3602:arXiv 3581:S2CID 3555:arXiv 3534:S2CID 3508:arXiv 3478:S2CID 3444:arXiv 3417:S2CID 3383:arXiv 3356:S2CID 3322:arXiv 3295:S2CID 3261:arXiv 3182:S2CID 3156:arXiv 3129:S2CID 3103:arXiv 3056:arXiv 3025:S2CID 2999:arXiv 2964:S2CID 2930:arXiv 2903:S2CID 2877:arXiv 2850:S2CID 2824:arXiv 2797:S2CID 2771:arXiv 2744:S2CID 2718:arXiv 2691:S2CID 2665:arXiv 2600:arXiv 2552:S2CID 2526:arXiv 2498:S2CID 2472:arXiv 2392:S2CID 2362:(PDF) 2298:(PDF) 2250:2 Dec 2122:9 May 1981:arXiv 1845:Notes 1378:Weber 1137:gluon 1064:in a 948:Hulse 888:Gödel 868:Milne 763:Milne 728:Gödel 425:Tests 250:from 209:from 194:from 168:from 159:metre 121:0.307 4439:, a 4424:here 3854:PMID 3470:PMID 3409:PMID 3348:PMID 3287:ISSN 3238:2017 3212:2017 3099:2016 2956:PMID 2638:PMID 2252:2010 2187:ISBN 2158:ISBN 2124:2019 2028:ISBN 1946:ISBN 1904:π / 1768:and 1740:VLBI 1734:and 1650:the 1630:and 1423:and 1364:and 1312:vR/c 1288:does 1174:also 1072:and 958:Taub 913:Kerr 853:Weyl 733:Kerr 651:BSSN 239:one 228:one 220:8.3 201:1.3 196:Moon 175:119 157:one 149:1.0 145:foot 143:one 137:Time 4418:in 4390:doi 4343:doi 4292:doi 4253:doi 4206:doi 4159:doi 4112:doi 4065:doi 4018:doi 3971:doi 3909:doi 3887:355 3846:doi 3791:doi 3729:doi 3707:312 3667:doi 3645:598 3620:doi 3598:590 3573:doi 3551:574 3526:doi 3504:556 3462:doi 3440:119 3401:doi 3379:119 3340:doi 3318:119 3279:doi 3174:doi 3152:765 3121:doi 3074:doi 3052:848 3017:doi 2995:355 2948:doi 2895:doi 2842:doi 2789:doi 2736:doi 2714:574 2683:doi 2661:598 2628:PMC 2618:doi 2544:doi 2490:doi 2468:267 2384:doi 2150:doi 1999:doi 1914:500 1911:429 1908:246 1901:651 1898:992 1896:999 1879:700 1876:870 1873:597 1871:149 1866:458 1863:792 1861:299 1746:of 1646:In 1391:000 1389:305 1316:v/c 1230:v/c 1159:). 1096:). 1056:In 968:Yau 646:ADM 293:000 291:100 276:000 222:min 211:Sun 110:173 97:000 94:000 92:671 79:000 77:186 64:000 61:000 58:080 38:458 35:792 33:299 4467:: 4426:). 4396:. 4388:. 4380:. 4368:28 4366:. 4349:. 4341:. 4333:. 4315:. 4298:. 4290:. 4282:. 4270:39 4268:. 4251:. 4243:. 4231:15 4229:. 4212:. 4204:. 4196:. 4184:13 4182:. 4165:. 4157:. 4149:. 4137:15 4135:. 4118:. 4110:. 4102:. 4090:13 4088:. 4071:. 4063:. 4055:. 4043:22 4041:. 4024:. 4016:. 4008:. 3996:21 3994:. 3977:. 3969:. 3961:. 3949:36 3947:. 3915:. 3907:. 3899:. 3885:. 3860:. 3852:. 3844:. 3836:. 3824:90 3822:. 3797:. 3789:. 3781:. 3769:21 3767:. 3735:. 3727:. 3719:. 3705:. 3673:. 3665:. 3657:. 3643:. 3626:. 3618:. 3610:. 3596:. 3579:. 3571:. 3563:. 3549:. 3532:. 3524:. 3516:. 3502:. 3476:. 3468:. 3460:. 3452:. 3438:. 3415:. 3407:. 3399:. 3391:. 3377:. 3354:. 3346:. 3338:. 3330:. 3316:. 3293:. 3285:. 3277:. 3269:. 3257:95 3255:. 3228:. 3202:. 3180:. 3172:. 3164:. 3150:. 3127:. 3119:. 3111:. 3097:. 3072:. 3064:. 3050:. 3046:. 3023:. 3015:. 3007:. 2993:. 2962:. 2954:. 2946:. 2938:. 2926:90 2924:. 2901:. 2893:. 2885:. 2873:65 2871:. 2848:. 2840:. 2832:. 2820:60 2818:. 2795:. 2787:. 2779:. 2767:36 2765:. 2742:. 2734:. 2726:. 2712:. 2689:. 2681:. 2673:. 2659:. 2636:. 2626:. 2616:. 2608:. 2594:. 2590:. 2550:. 2542:. 2534:. 2522:21 2520:. 2514:* 2496:. 2488:. 2480:. 2466:. 2422:. 2418:. 2390:. 2382:. 2372:21 2364:. 2328:28 2326:. 2306:19 2304:. 2300:. 2278:. 2274:. 2221:43 2215:. 2156:. 2144:. 2115:. 2087:^ 2079:49 2077:. 2073:. 2050:; 1997:. 1989:. 1975:. 1969:. 1906:10 1841:. 1820:EM 1815:− 1813:GW 1690:. 1520:. 1360:, 1356:, 1253:. 274:25 215:AU 177:ms 151:ns 4457:. 4450:. 4404:. 4392:: 4384:: 4374:: 4357:. 4345:: 4337:: 4327:: 4317:3 4306:. 4294:: 4286:: 4276:: 4259:. 4255:: 4247:: 4237:: 4220:. 4208:: 4200:: 4190:: 4173:. 4161:: 4153:: 4143:: 4126:. 4114:: 4106:: 4096:: 4079:. 4067:: 4059:: 4049:: 4032:. 4020:: 4012:: 4002:: 3985:. 3973:: 3965:: 3955:: 3938:. 3932:: 3923:. 3911:: 3903:: 3893:: 3879:c 3877:/ 3875:v 3868:. 3848:: 3840:: 3830:: 3816:c 3814:/ 3812:v 3805:. 3793:: 3785:: 3775:: 3758:. 3752:: 3743:. 3731:: 3723:: 3713:: 3696:. 3690:: 3681:. 3669:: 3661:: 3651:: 3634:. 3622:: 3614:: 3604:: 3587:. 3575:: 3567:: 3557:: 3540:. 3528:: 3520:: 3510:: 3484:. 3464:: 3456:: 3446:: 3423:. 3403:: 3395:: 3385:: 3362:. 3342:: 3334:: 3324:: 3301:. 3281:: 3273:: 3263:: 3240:. 3214:. 3188:. 3176:: 3168:: 3158:: 3135:. 3123:: 3115:: 3105:: 3082:. 3076:: 3068:: 3058:: 3031:. 3019:: 3011:: 3001:: 2987:c 2985:/ 2983:v 2970:. 2950:: 2942:: 2932:: 2909:. 2897:: 2889:: 2879:: 2856:. 2844:: 2836:: 2826:: 2803:. 2791:: 2783:: 2773:: 2750:. 2738:: 2730:: 2720:: 2697:. 2685:: 2677:: 2667:: 2644:. 2620:: 2612:: 2602:: 2596:4 2558:. 2546:: 2538:: 2528:: 2504:. 2492:: 2484:: 2474:: 2434:. 2430:: 2424:3 2404:. 2398:. 2386:: 2378:: 2280:2 2254:. 2195:. 2166:. 2152:: 2126:. 2036:. 2007:. 2001:: 1993:: 1983:: 1977:7 1954:. 1894:( 1859:( 1817:v 1810:v 1465:c 1439:c 1437:/ 1435:v 1337:c 1335:/ 1333:v 1329:v 1320:c 1308:c 1304:v 1300:R 1246:c 1242:c 1238:c 1234:v 1128:c 1124:c 1116:c 1094:c 1092:( 1042:e 1035:t 1028:v 709:) 705:( 378:T 369:= 357:g 350:+ 338:G 258:) 217:) 203:s 56:1

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index