298:
214:
40:
244:
279:
2978:
3733:
2447:
184:; the collimated jets about their polar axis; and the asymmetrical jets (relative to the orbital plane). All of those observed properties could be explained in terms of gravitomagnetic effects. Williams's application of Penrose's mechanism can be applied to black holes of any size. Relativistic jets can serve as the largest and brightest form of validations for gravitomagnetism.
2389:
297:
1304:
2784:
1725:
3289:
831:
2335:
Some higher-order gravitomagnetic effects can reproduce effects reminiscent of the interactions of more conventional polarized charges. For instance, if two wheels are spun on a common axis, the mutual gravitational attraction between the two wheels will be greater if they spin in opposite directions
144:
field, or velocity-dependent acceleration, is that a moving object near a massive, rotating object will experience acceleration that deviates from that predicted by a purely
Newtonian gravity (gravitoelectric) field. More subtle predictions, such as induced rotation of a falling object and precession
2304:
by â1. These factors variously modify the analogues of the equations for the
Lorentz force. There is no scaling choice that allows all the GEM and EM equations to be perfectly analogous. The discrepancy in the factors arises because the source of the gravitational field is the second order
939:
1573:
1168:
2973:{\displaystyle \mathbf {A} _{\text{g}}=-{\frac {G}{2c^{2}}}{\frac {\mathbf {L} \times \mathbf {r} }{r^{3}}}\quad {\text{with}}\quad \mathbf {L} ={\frac {2}{5}}mR^{2}\mathbf {\omega } \quad {\text{or}}\quad L=I_{\text{ball}}\omega ={\frac {2mR^{2}}{5}}{\frac {2\pi }{T}}\quad }
3829:
Note that the GEM equations are invariant under translations and spatial rotations, just not under boosts and more general curvilinear transformations. Maxwell's equations can be formulated in a way that makes them invariant under all of these coordinate transformations.
2363:
corkscrew-like gravitational field around the object. The reaction forces to dragging at the inner and outer equators would normally be expected to be equal and opposite in magnitude and direction respectively in the simpler case involving only minor-axis spin. When
1967:
3826:, there is no way to calculate the GEM variables of one such frame from the GEM variables of the other, unlike the situation with the variables of electromagnetism. Indeed, their predictions (about what motion is free fall) will probably conflict with each other.
2744:
2197:
3542:
1385:
641:
2351:" rotation) will tend to pull matter through the throat (a case of rotational frame dragging, acting through the throat). In theory, this configuration might be used for accelerating objects (through the throat) without such objects experiencing any
1579:
3149:
2040:
709:
2585:
3398:
701:
2258:
131:
different from that of a freely moving inertial body. This apparent field may be described by two components that act respectively like the electric and magnetic fields of electromagnetism, and by analogy these are called the
431:
837:
480:
3719:. When such fast motion and such strong gravitational fields exist in a system, the simplified approach of separating gravitomagnetic and gravitoelectric forces can be applied only as a very rough approximation.
1440:
2648:
2358:
Consider a toroidal mass with two degrees of rotation (both major axis and minor-axis spin, both turning inside out and revolving). This represents a "special case" in which gravitomagnetic effects generate a
1299:{\displaystyle \mathbf {E} _{\text{g}}:=-{\mbox{grad}}~\phi _{\text{g}}-{\frac {\partial \mathbf {A} _{\text{g}}}{\partial t}}=-\nabla ~\phi _{\text{g}}-{\frac {\partial \mathbf {A} _{\text{g}}}{\partial t}}}
2270:
The literature does not adopt a consistent scaling for the gravitoelectric and gravitomagnetic fields, making comparison tricky. For example, to obtain agreement with
Mashhoon's writings, all instances of
1452:
213:
3710:
527:
1775:
3067:
278:
1886:
2656:
2110:
1106:
Faraday's law of induction (third line of the table) and the
Gaussian law for the gravitomagnetic field (second line of the table) can be solved by the definition of a gravitation potential
565:
3428:
1315:
2776:
1852:
1160:
196:
3588:
573:
3715:
equals about 166 Hz. This would be easy to notice. However, the pulsar is spinning at a quarter of the speed of light at the equator, and its radius is only three times its
1720:{\displaystyle -{\frac {1}{c^{2}}}{\frac {\partial ^{2}\mathbf {A} _{\text{g}}}{\partial t^{2}}}+\nabla ^{2}~\mathbf {A} _{\text{g}}={\frac {4\pi G}{c^{2}}}\rho _{g}\mathbf {v} }
3284:{\displaystyle \mathbf {B} _{\text{g}}=\nabla \times \mathbf {A} _{\text{g}}={\frac {G}{2c^{2}}}{\frac {\mathbf {L} -3(\mathbf {L} \cdot \mathbf {r} /r)\mathbf {r} /r}{r^{3}}},}
2610:
1812:
243:
1131:
826:{\displaystyle \nabla \times \mathbf {B} _{\text{g}}-{\frac {1}{c^{2}}}{\frac {\partial \mathbf {E} _{\text{g}}}{\partial t}}=-{\frac {4\pi G}{c^{2}}}\mathbf {J} _{\text{g}}}
1973:
3006:
312:
of a solid sphere immersed in fluid, analogous directions and senses of rotation as magnetism, analogous interaction to frame dragging for the gravitomagnetic interaction.
5180:
3100:
2505:
5482:
140:
fields, since these arise in the same way around a mass that a moving electric charge is the source of electric and magnetic fields. The main consequence of the
3327:
647:
5288:
5125:
2203:
333:
produced by a rotating object (or any rotating massâenergy) can, in a particular limiting case, be described by equations that have the same form as in
4119:
5210:
4584:
3754:
2464:
934:{\displaystyle \nabla \times \mathbf {B} -{\frac {1}{c^{2}}}{\frac {\partial \mathbf {E} }{\partial t}}={\frac {1}{\epsilon _{0}c^{2}}}\mathbf {J} }
373:
104:
4605:
5786:
5459:
4181:
R.K. Williams (2001). "Collimated energyâmomentum extraction from rotating black holes in quasars and microquasars using the
Penrose mechanism".
1442:
into the
Gaussian law for the gravitation field (first line of the table) and AmpĂšre's circuital law (fourth line of the table) and applying the
5714:
5765:
5273:
437:
5791:
5443:
5416:
5258:
5173:
4966:
4923:
4738:
4716:
4694:
4675:
4532:
4505:
4437:
4295:
4017:
R.K. Williams (1995). "Extracting x rays, Îł rays, and relativistic ee pairs from supermassive Kerr black holes using the
Penrose mechanism".
3947:
3885:
2321:. This can be traced back to the spin-2 character of the gravitational field, in contrast to the electromagnetism being a spin-1 field. (See
3624:. Such a field is extremely weak and requires extremely sensitive measurements to be detected. One experiment to measure such field was the
1866:
is "small", in a stationary system, the net (Lorentz) force acting on it due to a GEM field is described by the following GEM analog to the
5848:
5536:
4709:
Causality, electromagnetic induction, and gravitation : a different approach to the theory of electromagnetic and gravitational fields
1393:
39:
5467:
2499:
A rotating spherical body with a homogeneous density distribution produces a stationary gravitomagnetic potential, which is described by:
4060:
R.K. Williams (2004). "Collimated escaping vortical polar ee jets intrinsically produced by rotating black holes and
Penrose processes".
5590:
2615:
1568:{\displaystyle -{\frac {1}{c^{2}}}{\frac {\partial ^{2}\phi _{\text{g}}}{\partial t^{2}}}+\nabla ^{2}~\phi _{\text{g}}=4\pi G\rho _{g}}
30:
This article is about the gravitational analog of electromagnetism as a whole. For the specific gravitational analog of magnetism, see
5771:
5319:
5302:
5243:
5424:
5253:
4653:
4634:
4615:
4594:
4238:
3780:
2486:
2428:
5166:
92:
effects of moving electric charge. The most common version of GEM is valid only far from isolated sources, and for slowly moving
5225:
5146:
3646:
488:
5531:
5453:
3758:
2468:
2368:
rotations are applied simultaneously, these two sets of reaction forces can be said to occur at different depths in a radial
5724:
3295:
1733:
173:
1962:{\displaystyle \mathbf {F} _{\text{g}}=m\left(\mathbf {E} _{\text{g}}\ +\mathbf {v} \times 4\mathbf {B} _{\text{g}}\right)}
99:
The analogy and equations differing only by some small factors were first published in 1893, before general relativity, by
5248:
3017:
2739:{\displaystyle \nabla ^{2}\mathbf {A} _{\text{g}}=-{\frac {4\pi G}{c^{2}}}\rho _{g}\mathbf {\omega } \times \mathbf {r} }
2410:
2399:
3922:
Unified Field
Mechanics: Natural Science Beyond the Veil of Spacetime, Morgan State University, USA, 16â19 November 2014
2406:
2375:
Modelling this complex behaviour as a curved spacetime problem has yet to be done and is believed to be very difficult.
2192:{\displaystyle {\mathcal {S}}_{\text{g}}=-{\frac {c^{2}}{4\pi G}}\mathbf {E} _{\text{g}}\times 4\mathbf {B} _{\text{g}}}
73:
5509:
5843:
5838:
5403:
5393:
5268:
3880:
2323:
5351:
3743:
5709:
5215:
4556:
3537:{\displaystyle B_{\text{g, Earth}}={\frac {G}{5c^{2}}}{\frac {m}{r}}{\frac {2\pi }{T}}={\frac {2\pi rg}{5c^{2}T}},}
3074:
1380:{\displaystyle \mathbf {B} _{\text{g}}:={\mbox{rot}}~\mathbf {A} _{\text{g}}=\nabla \times \mathbf {A} _{\text{g}}}
533:
334:
3762:
3747:
2457:
1854:
can also be solved for a rotating spherical body (which is a stationary case) leading to gravitomagnetic moments.
5503:
5498:
5719:
5429:
3816:
2306:
5606:
5600:
124:
77:
5567:
5122:
3870:
636:{\displaystyle \nabla \times \mathbf {E} _{\text{g}}+{\frac {\partial \mathbf {B} _{\text{g}}}{\partial t}}=0}
2752:
2372:
that extends across the rotating torus, making it more difficult to establish that cancellation is complete.
1828:
1136:
5634:
3860:
3597:
From this calculation it follows that the strength of the Earth's equatorial gravitomagnetic field is about
338:
181:
5435:
5345:
5007:
L. Filipe Costa; Carlos A. R. Herdeiro (2008). "A gravito-electromagnetic analogy based on tidal tensors".
3975:
3640:(which rotates 716 times per second), assuming a radius of 16 km and a mass of two solar masses, then
3550:
2336:
than in the same direction. This can be expressed as an attractive or repulsive gravitomagnetic component.
5551:
4901:
4663:
4415:
4273:
3794:
1069:
350:
5683:
5662:
5655:
5595:
2593:
1784:
5220:
4222:
145:
of a spinning object are among the last basic predictions of general relativity to be directly tested.
2035:{\displaystyle \mathbf {F} _{\text{e}}=q\left(\mathbf {E} \ +\ \mathbf {v} \times \mathbf {B} \right)}
1109:
5750:
5669:
5648:
5641:
5516:
5371:
5329:
5073:
5026:
4995:
4893:
4850:
4811:
4774:
4470:
4407:
4337:
4265:
4196:
4138:
4079:
4026:
3999:
3917:
3895:
3716:
5054:
A. Bakopoulos; P. Kanti (2016). "Novel
Ansatzes and Scalar Quantities in Gravito-Electromagnetism".
4278:
4906:
4420:
2360:
1819:
1081:
957:
342:
330:
188:
2989:
88:
is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the
5812:
5278:
5263:
5235:
5089:
5063:
5042:
5016:
4985:
4942:
4929:
4883:
4866:
4840:
4790:
4764:
4443:
4397:
4372:
4353:
4327:
4301:
4255:
4186:
4128:
4095:
4069:
3953:
3925:
3875:
3845:
3403:
3299:
357:, called the "GEM equations", can be derived. GEM equations compared to Maxwell's equations are:
326:
128:
120:
81:
66:
3591:
2580:{\displaystyle \nabla ^{2}\mathbf {A} _{\text{g}}=-{\frac {4\pi G}{c^{2}}}\rho _{g}\mathbf {v} }
4250:
B. Mashhoon; F. Gronwald; H.I.M. Lichtenegger (2001), "Gravitomagnetism and the Clock Effect",
3082:
5796:
5704:
5448:
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2314:
165:
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5472:
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5034:
4911:
4858:
4819:
4782:
4478:
4425:
4345:
4283:
4204:
4146:
4087:
4034:
3971:
3935:
3890:
3637:
3612:
3103:
3009:
1778:
1090:
354:
285:
250:
229:
149:
100:
62:
4880:
Reference Frames and Gravitomagnetism â Proceedings of the XXIII Spanish Relativity Meeting
4394:
Reference Frames and Gravitomagnetism â Proceedings of the XXIII Spanish Relativity Meeting
5477:
5398:
5358:
5324:
5129:
3865:
3855:
3625:
2344:
2091:
2078:
1060:
304:
264:
192:
169:
44:
3393:{\displaystyle \mathbf {B} _{\text{g}}={\frac {G}{2c^{2}}}{\frac {\mathbf {L} }{r^{3}}},}
5077:
5030:
4999:
4897:
4854:
4815:
4778:
4474:
4411:
4341:
4269:
4233:
Gravitation and Inertia, I. Ciufolini and J.A. Wheeler, Princeton Physics Series, 1995,
4200:
4142:
4083:
4030:
4003:
696:{\displaystyle \nabla \times \mathbf {E} +{\frac {\partial \mathbf {B} }{\partial t}}=0}
5677:
3850:
3618:
2369:
1094:
1007:
985:
967:
346:
309:
255:
157:
93:
89:
31:
5141:
Measurement of Gravitomagnetic and Acceleration Fields Around Rotating Superconductors
4831:
R.T. Jantzen; P. Carini; D. Bini (1992). "The Many Faces of Gravitoelectromagnetism".
4786:
4349:
1822:. In this way GEM can be regarded as a generalization of Newton's gravitation theory.
5832:
5614:
5283:
5151:
5112:
5093:
4933:
4862:
4447:
3991:
3957:
3823:
3822:
Although GEM may hold approximately in two different reference frames connected by a
2059:
1867:
1818:
is obtained under non-stationary conditions. GEM therefore predicts the existence of
1815:
153:
5046:
4794:
4357:
4305:
195:
satellite experiment, to see whether they are consistent with gravitomagnetism. The
5572:
5381:
4870:
4099:
3840:
3309:-factor by taking into account relativistic calculations. At the equatorial plane,
3305:
is two. This factor of two can be explained completely analogous to the electron's
2310:
2253:{\displaystyle {\mathcal {S}}=c^{2}\varepsilon _{0}\mathbf {E} \times \mathbf {B} }
1443:
148:
Indirect validations of gravitomagnetic effects have been derived from analyses of
4524:
Inertia and gravitation : the fundamental nature and structure of spaceâtime
5541:
4166:
R.K. Williams (2005). "Gravitomagnetic field and Penrose scattering processes".
3812:
3732:
3318:
2446:
116:
69:
17:
5038:
4915:
4755:
S.J. Clark; R.W. Tucker (2000). "Gauge symmetry and gravito-electromagnetism".
4429:
4318:
S.J. Clark; R.W. Tucker (2000). "Gauge symmetry and gravito-electromagnetism".
3939:
3594:. The field direction coincides with the angular moment direction, i.e. north.
5755:
5085:
4151:
4114:
2348:
2309:, as opposed to the source of the electromagnetic field being the first order
426:{\displaystyle \nabla \cdot \mathbf {E} _{\text{g}}=-4\pi G\rho _{\text{g}}\ }
161:
4542:
4038:
2313:
tensor. This difference becomes clearer when one compares non-invariance of
5760:
5742:
5546:
5523:
4287:
1019:
4046:
5158:
4522:
5817:
5627:
5620:
5140:
4252:
Gyros, Clocks, Interferometers ...: Testing Relativistic Gravity in Space
4191:
4074:
2055:
1050:
5135:
475:{\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\epsilon _{0}}}}
5189:
3419:
2471: in this section. Unsourced material may be challenged and removed.
2352:
997:
58:
5021:
4990:
4947:
4888:
4845:
4823:
4769:
4482:
4402:
4377:
4332:
4260:
4208:
3123:
2340:
1435:{\displaystyle \left(\phi _{\text{g}},\mathbf {A} _{\text{g}}\right)}
177:
4223:
https://www.slac.stanford.edu/pubs/slacpubs/14750/slac-pub-14775.pdf
2778:. The analytical solution outside of the body is (see for example):
5068:
4976:
M. Tajmar; C.J. de Matos (2001). "Gravitomagnetic Barnett Effect".
4133:
4091:
3977:
Electromagnetic Theory: A Gravitational and Electromagnetic Analogy
3930:
191:
is currently analyzing data from the first direct test of GEM, the
168:, University of Florida, developed a rigorous proof that validated
5409:
3994:(1969). "Gravitational collapse: The role of general relativity".
3415:
2643:{\displaystyle \mathbf {v} =\mathbf {\omega } \times \mathbf {r} }
160:-related effects for extracting energy and momentum from rotating
176:
could account for the observed high energies and luminosities of
5107:
4557:"2*pi*radius of Earth*earth gravity/(5*c^2*day) â Google Search"
3113:
2339:
Gravitomagnetic arguments also predict that a flexible or fluid
2068:
5162:
5136:
Gravitomagnetic London Moment â New test of General Relativity?
4941:
B. Mashhoon (2003). "Gravitoelectromagnetism: a Brief Review".
4371:
B. Mashhoon (2008). "Gravitoelectromagnetism: A Brief Review".
5116:
3726:
2440:
2382:
1781:
of the classical gravitation theory is obtained. In a vacuum (
337:. Starting from the basic equation of general relativity, the
4646:
Spacetime and Geometry: An Introduction to General Relativity
76:
and an approximation, valid under certain conditions, to the
4254:, Lecture Notes in Physics, vol. 562, pp. 83â108,
2209:
2117:
3406:
have equal gravitomagnetic and gravitoelectric components.
3298:
rate. This suggests that the gravitomagnetic analog of the
291:, same field profile, and field generation due to rotation.
4521:
Pfister, Herbert, 1936-; King, Markus (24 February 2015).
43:
Diagram regarding the confirmation of gravitomagnetism by
27:
Analogies between Maxwell's and Einstein's field equations
5147:
Test of the LenseâThirring effect with the MGS Mars probe
4627:
Gravity: An Introduction to Einstein's General Relativity
2749:
has to be solved to obtain the gravitomagnetic potential
1446:
the following inhomogeneous wave-equations are obtained:
3705:{\displaystyle B_{\text{g}}={\frac {2\pi Gm}{5rc^{2}T}}}
2090:
The GEM Poynting vector compared to the electromagnetic
522:{\displaystyle \nabla \cdot \mathbf {B} _{\text{g}}=0\ }
4583:
M. P. Hobson; G. P. Efstathiou; A. N. Lasenby (2006).
3918:"Pre-metric electromagnetism as a path to unification"
1770:{\displaystyle \partial \phi _{\text{g}}/\partial t=0}
1335:
1191:
197:
Apache Point Observatory Lunar Laser-ranging Operation
3649:
3553:
3431:
3330:
3152:
3085:
3020:
2992:
2787:
2755:
2659:
2618:
2596:
2508:
2409:. Please help to ensure that disputed statements are
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2113:
1976:
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1171:
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576:
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491:
440:
376:
4959:
Measuring Gravitomagnetism: A Challenging Enterprise
4687:
Measuring Gravitomagnetism: A Challenging Enterprise
3062:{\displaystyle I_{\text{ball}}={\frac {2mR^{2}}{5}}}
1825:
The wave equation for the gravitomagnetic potential
5805:
5737:
5695:
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5491:
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5312:
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5203:
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5115:
news on tentative result of European Space Agency (
5113:Gyroscopic Superconducting Gravitomagnetic Effects
4802:R.L. Forward (1963). "Guidelines to Antigravity".
4666:(1990). "Gravity's next prize: Gravitomagnetism".
4586:General Relativity: An Introduction for Physicists
4461:R.L. Forward (1963). "Guidelines to Antigravity".
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4670:. Scientific American Library. pp. 232â233.
3980:. Vol. 1. The Electrician. pp. 455â464.
3636:If the preceding formula is used with the pulsar
2612:the velocity inside the body can be described as
4610:. Cambridge University Press. pp. 200â207.
4589:. Cambridge University Press. pp. 490â491.
199:also plans to observe gravitomagnetism effects.
4878:B. Mashhoon (2000). "Gravitoelectromagnetism".
4392:B. Mashhoon (2000). "Gravitoelectromagnetism".
5483:Degenerate Higher-Order Scalar-Tensor theories
3793:While Maxwell's equations are invariant under
2379:Gravitomagnetic fields of astronomical objects
5174:
3891:Speed of gravity § Electrodynamical analogies
560:{\displaystyle \nabla \cdot \mathbf {B} =0\ }
8:
5108:Gravity Probe B: Testing Einstein's Universe
4221:Gravitomagnetism in Quantum Mechanics, 2014
3797:, the GEM equations are not. The fact that
2278:in the GEM equations must be multiplied by â
978:is the gravitomagnetic field, with SI unit s
4115:"Gravitational fields of the magnetic-type"
3761:. Unsourced material may be challenged and
2327:for more on "spin-1" and "spin-2" fields).
956:is the gravitoelectric field (conventional
5309:
5200:
5181:
5167:
5159:
4168:Annals of the New York Academy of Sciences
3136:The formula for the gravitomagnetic field
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4120:International Journal of Modern Physics D
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3781:Learn how and when to remove this message
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2134:
2122:
2116:
2115:
2112:
2022:
2014:
2000:
1983:
1978:
1975:
1948:
1943:
1931:
1919:
1914:
1896:
1891:
1888:
1838:
1833:
1830:
1792:
1786:
1750:
1744:
1735:
1712:
1706:
1694:
1677:
1668:
1663:
1653:
1637:
1622:
1617:
1610:
1603:
1595:
1586:
1581:
1559:
1537:
1524:
1508:
1493:
1483:
1476:
1468:
1459:
1454:
1421:
1416:
1406:
1395:
1371:
1366:
1350:
1345:
1334:
1325:
1320:
1317:
1279:
1274:
1267:
1258:
1225:
1220:
1213:
1204:
1190:
1178:
1173:
1170:
1146:
1141:
1138:
1117:
1111:
926:
917:
907:
897:
878:
872:
864:
855:
847:
839:
817:
812:
803:
786:
763:
758:
751:
743:
734:
725:
720:
711:
671:
665:
657:
649:
610:
605:
598:
589:
584:
575:
543:
535:
504:
499:
490:
464:
455:
447:
439:
414:
389:
384:
375:
2405:Relevant discussion may be found on the
2096:
1872:
359:
156:had proposed a mechanism that relies on
38:
5787:Gravitational interaction of antimatter
3908:
3815:(instead they are merely a part of the
3321:vanishes, and this formula reduces to:
2771:{\displaystyle \mathbf {A} _{\text{g}}}
2347:rotational acceleration (accelerating "
1847:{\displaystyle \mathbf {A} _{\text{g}}}
1155:{\displaystyle \mathbf {A} _{\text{g}}}
209:
1053:of the mass flow), with SI unit kgâ
mâ
s
5792:Physics in the medieval Islamic world
5715:(2+1)-dimensional topological gravity
5211:Newton's law of universal gravitation
4629:. Addison-Wesley. pp. 296, 303.
3886:Non-Relativistic Gravitational Fields
3583:{\displaystyle g=G{\frac {m}{r^{2}}}}
105:Newton's law of universal gravitation
7:
5537:Asymptotic safety in quantum gravity
4668:A journey into gravity and spacetime
3759:adding citations to reliable sources
2469:adding citations to reliable sources
127:makes an apparent field appear in a
5143:M. Tajmar, et al., 17 October 2006.
4185:. Vol. 586. pp. 448â453.
4170:. Vol. 1045. pp. 232â245.
3819:) is the basis of this difference.
2590:Due to the body's angular velocity
5289:GibbonsâHawkingâYork boundary term
5056:General Relativity and Gravitation
4607:Introduction to General Relativity
4498:Elektromagnetismus und Gravitation
3168:
2661:
2605:{\displaystyle \mathbf {\omega } }
2510:
1807:{\displaystyle \rho _{\text{g}}=0}
1755:
1737:
1650:
1630:
1607:
1521:
1501:
1480:
1359:
1287:
1270:
1248:
1233:
1216:
885:
875:
841:
771:
754:
713:
678:
668:
651:
618:
601:
577:
537:
492:
441:
377:
115:This approximate reformulation of
25:
5404:Modified Newtonian dynamics, MOND
5320:Classical theories of gravitation
4500:(2. ed.). Springer-Vieweg.
3731:
3418:'s gravitomagnetic field at its
3371:
3333:
3253:
3237:
3229:
3215:
3176:
3155:
2994:
2865:
2840:
2832:
2790:
2758:
2732:
2672:
2636:
2620:
2573:
2521:
2445:
2387:
2246:
2238:
2179:
2161:
2023:
2015:
2001:
1979:
1944:
1932:
1915:
1892:
1834:
1713:
1664:
1618:
1417:
1367:
1346:
1321:
1275:
1221:
1174:
1142:
1126:{\displaystyle \phi _{\text{g}}}
927:
879:
848:
813:
759:
721:
672:
658:
606:
585:
544:
500:
448:
385:
296:
277:
242:
212:
5226:History of gravitational theory
4648:. Addison-Wesley. p. 281.
4527:. Cham: Springer. p. 147.
2969:
2906:
2900:
2863:
2857:
2456:needs additional citations for
1862:For a test particle whose mass
1390:Inserting this four potentials
1091:speed of propagation of gravity
349:, the gravitational analogs to
103:as a separate theory expanding
5532:Causal dynamical triangulation
5221:Poisson's equation for gravity
3998:. Numero Speciale 1: 252â276.
3249:
3225:
1:
5123:In Search of Gravitomagnetism
4757:Classical and Quantum Gravity
4731:Gravitation and Cogravitation
4320:Classical and Quantum Gravity
4863:10.1016/0003-4916(92)90297-Y
3414:Therefore, the magnitude of
3317:are perpendicular, so their
3073:of a ball-shaped body (see:
3001:{\displaystyle \mathbf {L} }
1730:For a stationary situation (
204:Physical analogues of fields
5849:Tests of general relativity
5394:Infinite derivative gravity
4978:Indian Journal of Physics B
4804:American Journal of Physics
4787:10.1088/0264-9381/17/19/311
4463:American Journal of Physics
4350:10.1088/0264-9381/17/19/311
3881:Modified Newtonian dynamics
2324:Relativistic wave equations
1018:is mass current density or
172:. Her model showed how the
5865:
5582:Unified-field-theoric and
5039:10.1103/PhysRevD.78.024021
4916:10.1142/9789812810021_0009
4430:10.1142/9789812810021_0009
4183:AIP Conference Proceedings
3940:10.1142/9789814719063_0023
3294:It is exactly half of the
3075:list of moments of inertia
335:classical electromagnetism
61:between the equations for
29:
5725:JackiwâTeitelboim gravity
5504:Canonical quantum gravity
5499:Euclidean quantum gravity
5086:10.1007/s10714-017-2207-x
4152:10.1142/S0218271820430014
4062:The Astrophysical Journal
3996:Rivista del Nuovo Cimento
3916:David Delphenich (2015).
3296:LenseâThirring precession
3132:is the rotational period.
3095:{\displaystyle \omega \ }
1133:and the vector potential
74:Maxwell's field equations
45:Gravity Probe B
5601:Superfluid vacuum theory
5425:Nonsymmetric gravitation
5274:Post-Newtonian formalism
4961:. Nova. pp. 29â39.
4039:10.1103/PhysRevD.51.5387
3143:can now be obtained by:
222:â gravitomagnetic field
78:Einstein field equations
72:; specifically: between
5766:Mechanical explanations
5635:Heterotic string theory
5591:Noncommutative geometry
5510:WheelerâDeWitt equation
5236:General relativity (GR)
5216:Gauss's law for gravity
5190:Theories of gravitation
4733:. Electret Scientific.
4711:. Electret Scientific.
4288:10.1007/3-540-40988-2_5
3861:Gravitational radiation
3795:Lorentz transformations
339:Einstein field equation
51:Gravitoelectromagnetism
5607:Logarithmic BEC vacuum
5552:Rainbow gravity theory
5430:Scalarâtensor theories
5204:Newtonian gravity (NG)
5132:, NASA, 20 April 2004.
5128:9 October 2006 at the
4957:L. Iorio, ed. (2007).
4685:L. Iorio, ed. (2007).
3706:
3584:
3538:
3394:
3285:
3096:
3063:
3002:
2974:
2772:
2740:
2644:
2606:
2581:
2254:
2193:
2036:
1963:
1848:
1808:
1771:
1721:
1569:
1436:
1381:
1300:
1156:
1127:
1070:gravitational constant
935:
827:
697:
637:
561:
523:
476:
427:
341:, and assuming a weak
284:... or, equivalently,
182:active galactic nuclei
47:
5684:Twistor string theory
5663:Type II string theory
5656:Bosonic string theory
5596:Semiclassical gravity
5561:Unified-field-theoric
5346:Poincaré gauge theory
4625:J. B. Hartle (2002).
4496:A. Malcherek (2023).
4113:Danehkar, A. (2020).
3707:
3585:
3539:
3395:
3286:
3097:
3064:
3003:
2975:
2773:
2741:
2645:
2607:
2582:
2255:
2194:
2081:of the test particle.
2037:
1964:
1849:
1809:
1772:
1722:
1570:
1437:
1382:
1301:
1157:
1128:
936:
828:
698:
638:
562:
524:
477:
428:
174:LenseâThirring effect
57:, refers to a set of
42:
5751:Aristotelian physics
5720:GaussâBonnet gravity
5670:Little string theory
5649:Type 0 string theory
5642:Type I string theory
5517:Loop quantum gravity
5444:Scalarâtensorâvector
5417:Tensorâvectorâscalar
5372:Gauge theory gravity
5330:Theory of everything
4882:. pp. 121â132.
4604:L. H. Ryder (2009).
4396:. pp. 121â132.
3896:Stationary spacetime
3817:stressâenergy tensor
3755:improve this section
3717:Schwarzschild radius
3647:
3551:
3429:
3328:
3150:
3083:
3018:
2990:
2785:
2753:
2657:
2616:
2594:
2506:
2465:improve this article
2398:factual accuracy is
2331:Higher-order effects
2307:stressâenergy tensor
2204:
2111:
2071:of the test particle
1974:
1887:
1829:
1785:
1734:
1580:
1453:
1394:
1316:
1169:
1137:
1110:
838:
710:
648:
574:
534:
489:
438:
374:
366:Maxwell's equations
5568:KaluzaâKlein theory
5078:2017GReGr..49...44B
5031:2008PhRvD..78b4021C
5000:2000gr.qc....12091D
4898:2001rfg..conf..121M
4855:1992AnPhy.215....1J
4816:1963AmJPh..31..166F
4779:2000CQGra..17.4125C
4644:S. Carroll (2003).
4475:1963AmJPh..31..166F
4412:2001rfg..conf..121M
4342:2000CQGra..17.4125C
4270:2001LNP...562...83M
4201:2001AIPC..586..448W
4143:2020IJMPD..2943001D
4084:2004ApJ...611..952W
4031:1995PhRvD..51.5387W
4004:1969NCimR...1..252P
3871:KaluzaâKlein theory
3404:Gravitational waves
1820:gravitational waves
1082:vacuum permittivity
1000:, with SI unit kgâ
m
960:), with SI unit mâ
s
958:gravitational field
351:Maxwell's equations
343:gravitational field
331:gravitational field
189:Stanford University
170:Penrose's mechanism
5844:Effects of gravity
5839:General relativity
5813:Gravitational wave
5696:Generalisations /
5584:quantum-mechanical
5492:Quantum-mechanical
5305:general relativity
5279:Linearized gravity
3876:Linearized gravity
3846:Artificial gravity
3723:Lack of invariance
3702:
3580:
3534:
3390:
3281:
3092:
3059:
2998:
2970:
2768:
2736:
2640:
2602:
2577:
2250:
2189:
2032:
1959:
1844:
1804:
1767:
1717:
1565:
1432:
1377:
1339:
1296:
1195:
1152:
1123:
931:
823:
693:
633:
557:
519:
472:
423:
327:general relativity
129:frame of reference
121:general relativity
82:general relativity
48:
5826:
5825:
5797:Theory of impetus
5733:
5732:
5705:Liouville gravity
5449:Conformal gravity
5377:Composite gravity
5367:Bimetric theories
5297:
5296:
5009:Physical Review D
4968:978-1-60021-002-0
4925:978-981-02-4631-0
4833:Annals of Physics
4824:10.1119/1.1969340
4763:(19): 4125â4157.
4740:978-0-917406-15-7
4718:978-0-917406-09-6
4696:978-1-60021-002-0
4677:978-0-7167-5016-1
4534:978-3-319-15036-9
4507:978-3-658-42701-6
4483:10.1119/1.1969340
4439:978-981-02-4631-0
4326:(19): 4125â4157.
4297:978-3-540-41236-6
4209:10.1063/1.1419591
4025:(10): 5387â5427.
3949:978-981-4719-05-6
3791:
3790:
3783:
3700:
3657:
3578:
3529:
3490:
3475:
3465:
3439:
3385:
3366:
3340:
3276:
3209:
3183:
3162:
3091:
3071:moment of inertia
3057:
3028:
2967:
2952:
2920:
2904:
2880:
2861:
2855:
2826:
2797:
2765:
2711:
2679:
2560:
2528:
2497:
2496:
2489:
2439:
2438:
2431:
2319:charge invariance
2315:relativistic mass
2266:Scaling of fields
2263:
2262:
2186:
2168:
2157:
2125:
2045:
2044:
2013:
2007:
1986:
1951:
1927:
1922:
1899:
1841:
1795:
1747:
1700:
1671:
1661:
1644:
1625:
1601:
1540:
1532:
1515:
1496:
1474:
1424:
1409:
1374:
1353:
1343:
1338:
1328:
1294:
1282:
1261:
1253:
1240:
1228:
1207:
1199:
1194:
1181:
1149:
1120:
944:
943:
924:
892:
870:
820:
809:
778:
766:
749:
728:
685:
625:
613:
592:
556:
518:
507:
470:
422:
417:
392:
166:Reva Kay Williams
150:relativistic jets
16:(Redirected from
5856:
5781:
5779:Entropic gravity
5774:
5698:extensions of GR
5686:
5672:
5665:
5658:
5651:
5644:
5637:
5630:
5623:
5609:
5526:
5519:
5512:
5473:Geometrodynamics
5462:
5438:
5419:
5412:
5361:
5354:
5310:
5201:
5183:
5176:
5169:
5160:
5097:
5071:
5050:
5024:
5003:
4993:
4972:
4952:
4950:
4937:
4909:
4891:
4874:
4848:
4827:
4798:
4772:
4744:
4722:
4700:
4681:
4659:
4640:
4621:
4600:
4565:
4564:
4553:
4547:
4546:
4518:
4512:
4511:
4493:
4487:
4486:
4458:
4452:
4451:
4423:
4405:
4389:
4383:
4382:
4380:
4368:
4362:
4361:
4335:
4315:
4309:
4308:
4281:
4263:
4247:
4241:
4231:
4225:
4219:
4213:
4212:
4194:
4192:astro-ph/0111161
4178:
4172:
4171:
4163:
4157:
4156:
4154:
4136:
4110:
4104:
4103:
4077:
4075:astro-ph/0404135
4057:
4051:
4050:
4014:
4008:
4007:
3988:
3982:
3981:
3968:
3962:
3961:
3933:
3913:
3786:
3779:
3775:
3772:
3766:
3735:
3727:
3711:
3709:
3708:
3703:
3701:
3699:
3695:
3694:
3678:
3664:
3659:
3658:
3655:
3638:PSR J1748-2446ad
3623:
3610:
3604:
3602:
3589:
3587:
3586:
3581:
3579:
3577:
3576:
3564:
3543:
3541:
3540:
3535:
3530:
3528:
3524:
3523:
3510:
3496:
3491:
3486:
3478:
3476:
3468:
3466:
3464:
3463:
3462:
3446:
3441:
3440:
3437:
3399:
3397:
3396:
3391:
3386:
3384:
3383:
3374:
3369:
3367:
3365:
3364:
3363:
3347:
3342:
3341:
3338:
3336:
3290:
3288:
3287:
3282:
3277:
3275:
3274:
3265:
3261:
3256:
3245:
3240:
3232:
3218:
3212:
3210:
3208:
3207:
3206:
3190:
3185:
3184:
3181:
3179:
3164:
3163:
3160:
3158:
3104:angular velocity
3101:
3099:
3098:
3093:
3089:
3068:
3066:
3065:
3060:
3058:
3053:
3052:
3051:
3035:
3030:
3029:
3026:
3010:angular momentum
3007:
3005:
3004:
2999:
2997:
2979:
2977:
2976:
2971:
2968:
2963:
2955:
2953:
2948:
2947:
2946:
2930:
2922:
2921:
2918:
2905:
2902:
2899:
2894:
2893:
2881:
2873:
2868:
2862:
2859:
2856:
2854:
2853:
2844:
2843:
2835:
2829:
2827:
2825:
2824:
2823:
2807:
2799:
2798:
2795:
2793:
2777:
2775:
2774:
2769:
2767:
2766:
2763:
2761:
2745:
2743:
2742:
2737:
2735:
2727:
2722:
2721:
2712:
2710:
2709:
2700:
2689:
2681:
2680:
2677:
2675:
2669:
2668:
2649:
2647:
2646:
2641:
2639:
2631:
2623:
2611:
2609:
2608:
2603:
2601:
2586:
2584:
2583:
2578:
2576:
2571:
2570:
2561:
2559:
2558:
2549:
2538:
2530:
2529:
2526:
2524:
2518:
2517:
2492:
2485:
2481:
2478:
2472:
2449:
2441:
2434:
2427:
2423:
2420:
2414:
2411:reliably sourced
2391:
2390:
2383:
2343:mass undergoing
2296:
2294:
2293:
2287:
2284:
2259:
2257:
2256:
2251:
2249:
2241:
2236:
2235:
2226:
2225:
2213:
2212:
2198:
2196:
2195:
2190:
2188:
2187:
2184:
2182:
2170:
2169:
2166:
2164:
2158:
2156:
2145:
2144:
2135:
2127:
2126:
2123:
2121:
2120:
2097:
2041:
2039:
2038:
2033:
2031:
2027:
2026:
2018:
2011:
2005:
2004:
1988:
1987:
1984:
1982:
1968:
1966:
1965:
1960:
1958:
1954:
1953:
1952:
1949:
1947:
1935:
1925:
1924:
1923:
1920:
1918:
1901:
1900:
1897:
1895:
1873:
1853:
1851:
1850:
1845:
1843:
1842:
1839:
1837:
1813:
1811:
1810:
1805:
1797:
1796:
1793:
1779:Poisson equation
1776:
1774:
1773:
1768:
1754:
1749:
1748:
1745:
1726:
1724:
1723:
1718:
1716:
1711:
1710:
1701:
1699:
1698:
1689:
1678:
1673:
1672:
1669:
1667:
1659:
1658:
1657:
1645:
1643:
1642:
1641:
1628:
1627:
1626:
1623:
1621:
1615:
1614:
1604:
1602:
1600:
1599:
1587:
1574:
1572:
1571:
1566:
1564:
1563:
1542:
1541:
1538:
1530:
1529:
1528:
1516:
1514:
1513:
1512:
1499:
1498:
1497:
1494:
1488:
1487:
1477:
1475:
1473:
1472:
1460:
1441:
1439:
1438:
1433:
1431:
1427:
1426:
1425:
1422:
1420:
1411:
1410:
1407:
1386:
1384:
1383:
1378:
1376:
1375:
1372:
1370:
1355:
1354:
1351:
1349:
1341:
1340:
1336:
1330:
1329:
1326:
1324:
1305:
1303:
1302:
1297:
1295:
1293:
1285:
1284:
1283:
1280:
1278:
1268:
1263:
1262:
1259:
1251:
1241:
1239:
1231:
1230:
1229:
1226:
1224:
1214:
1209:
1208:
1205:
1197:
1196:
1192:
1183:
1182:
1179:
1177:
1161:
1159:
1158:
1153:
1151:
1150:
1147:
1145:
1132:
1130:
1129:
1124:
1122:
1121:
1118:
940:
938:
937:
932:
930:
925:
923:
922:
921:
912:
911:
898:
893:
891:
883:
882:
873:
871:
869:
868:
856:
851:
832:
830:
829:
824:
822:
821:
818:
816:
810:
808:
807:
798:
787:
779:
777:
769:
768:
767:
764:
762:
752:
750:
748:
747:
735:
730:
729:
726:
724:
702:
700:
699:
694:
686:
684:
676:
675:
666:
661:
642:
640:
639:
634:
626:
624:
616:
615:
614:
611:
609:
599:
594:
593:
590:
588:
566:
564:
563:
558:
554:
547:
528:
526:
525:
520:
516:
509:
508:
505:
503:
481:
479:
478:
473:
471:
469:
468:
456:
451:
432:
430:
429:
424:
420:
419:
418:
415:
394:
393:
390:
388:
360:
355:electromagnetism
300:
290:
281:
271:
262:
251:Electromagnetism
246:
236:
230:angular momentum
227:
220:Gravitomagnetism
216:
125:weak field limit
119:as described by
101:Oliver Heaviside
86:Gravitomagnetism
63:electromagnetism
59:formal analogies
21:
18:Gravitomagnetism
5864:
5863:
5859:
5858:
5857:
5855:
5854:
5853:
5829:
5828:
5827:
5822:
5801:
5777:
5770:
5741:
5739:
5729:
5710:Lovelock theory
5697:
5691:
5682:
5668:
5661:
5654:
5647:
5640:
5633:
5626:
5619:
5605:
5583:
5577:
5556:
5522:
5515:
5508:
5487:
5478:Induced gravity
5458:
5454:Scalar theories
5434:
5415:
5408:
5399:Massive gravity
5359:Teleparallelism
5357:
5352:EinsteinâCartan
5350:
5334:
5325:Quantum gravity
5304:
5303:Alternatives to
5293:
5259:Exact solutions
5230:
5192:
5187:
5155:, January 2007.
5130:Wayback Machine
5104:
5053:
5006:
4975:
4969:
4956:
4940:
4926:
4877:
4830:
4801:
4754:
4751:
4741:
4725:
4719:
4703:
4697:
4684:
4678:
4662:
4656:
4643:
4637:
4624:
4618:
4603:
4597:
4582:
4579:
4574:
4572:Further reading
4569:
4568:
4555:
4554:
4550:
4535:
4520:
4519:
4515:
4508:
4495:
4494:
4490:
4460:
4459:
4455:
4440:
4391:
4390:
4386:
4370:
4369:
4365:
4317:
4316:
4312:
4298:
4279:10.1.1.340.8408
4249:
4248:
4244:
4232:
4228:
4220:
4216:
4180:
4179:
4175:
4165:
4164:
4160:
4127:(14): 2043001.
4112:
4111:
4107:
4059:
4058:
4054:
4019:Physical Review
4016:
4015:
4011:
3990:
3989:
3985:
3970:
3969:
3965:
3950:
3915:
3914:
3910:
3905:
3900:
3866:Gravity Probe B
3856:Geodetic effect
3836:
3810:
3803:
3787:
3776:
3770:
3767:
3752:
3736:
3725:
3686:
3679:
3665:
3650:
3645:
3644:
3634:
3626:Gravity Probe B
3608:
3606:
3600:
3598:
3592:Earth's gravity
3568:
3549:
3548:
3515:
3511:
3497:
3479:
3454:
3450:
3432:
3427:
3426:
3412:
3375:
3355:
3351:
3331:
3326:
3325:
3266:
3213:
3198:
3194:
3174:
3153:
3148:
3147:
3142:
3081:
3080:
3043:
3036:
3021:
3016:
3015:
2988:
2987:
2956:
2938:
2931:
2913:
2885:
2845:
2830:
2815:
2811:
2788:
2783:
2782:
2756:
2751:
2750:
2713:
2701:
2690:
2670:
2660:
2655:
2654:
2614:
2613:
2592:
2591:
2562:
2550:
2539:
2519:
2509:
2504:
2503:
2493:
2482:
2476:
2473:
2462:
2450:
2435:
2424:
2418:
2415:
2404:
2396:This section's
2392:
2388:
2381:
2333:
2303:
2288:
2285:
2282:
2281:
2279:
2277:
2268:
2227:
2217:
2202:
2201:
2177:
2159:
2146:
2136:
2114:
2109:
2108:
2092:Poynting vector
2088:
2086:Poynting vector
2079:electric charge
1999:
1995:
1977:
1972:
1971:
1942:
1913:
1912:
1908:
1890:
1885:
1884:
1860:
1832:
1827:
1826:
1788:
1783:
1782:
1740:
1732:
1731:
1702:
1690:
1679:
1662:
1649:
1633:
1629:
1616:
1606:
1605:
1591:
1578:
1577:
1555:
1533:
1520:
1504:
1500:
1489:
1479:
1478:
1464:
1451:
1450:
1415:
1402:
1401:
1397:
1392:
1391:
1365:
1344:
1319:
1314:
1313:
1286:
1273:
1269:
1254:
1232:
1219:
1215:
1200:
1172:
1167:
1166:
1140:
1135:
1134:
1113:
1108:
1107:
1104:
1079:
1061:current density
1048:
1041:
1035:
1028:
1017:
995:
977:
955:
913:
903:
902:
884:
874:
860:
836:
835:
811:
799:
788:
770:
757:
753:
739:
719:
708:
707:
677:
667:
646:
645:
617:
604:
600:
583:
572:
571:
532:
531:
498:
487:
486:
460:
436:
435:
410:
383:
372:
371:
323:
318:
317:
316:
313:
305:Fluid mechanics
301:
292:
288:
282:
273:
267:
258:
247:
238:
232:
228:due to (total)
223:
217:
206:
205:
193:Gravity Probe B
142:gravitomagnetic
138:gravitomagnetic
134:gravitoelectric
113:
35:
28:
23:
22:
15:
12:
11:
5:
5862:
5860:
5852:
5851:
5846:
5841:
5831:
5830:
5824:
5823:
5821:
5820:
5815:
5809:
5807:
5806:Related topics
5803:
5802:
5800:
5799:
5794:
5789:
5784:
5783:
5782:
5775:
5763:
5758:
5753:
5747:
5745:
5735:
5734:
5731:
5730:
5728:
5727:
5722:
5717:
5712:
5707:
5701:
5699:
5693:
5692:
5690:
5689:
5688:
5687:
5678:Twistor theory
5675:
5674:
5673:
5666:
5659:
5652:
5645:
5638:
5631:
5624:
5612:
5611:
5610:
5598:
5593:
5587:
5585:
5579:
5578:
5576:
5575:
5570:
5564:
5562:
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5557:
5555:
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5549:
5544:
5539:
5534:
5529:
5528:
5527:
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5501:
5495:
5493:
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5486:
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5465:
5464:
5463:
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5441:
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5439:
5427:
5422:
5421:
5420:
5413:
5401:
5396:
5391:
5379:
5374:
5369:
5364:
5363:
5362:
5355:
5342:
5340:
5336:
5335:
5333:
5332:
5327:
5322:
5316:
5314:
5307:
5299:
5298:
5295:
5294:
5292:
5291:
5286:
5281:
5276:
5271:
5266:
5261:
5256:
5251:
5246:
5240:
5238:
5232:
5231:
5229:
5228:
5223:
5218:
5213:
5207:
5205:
5198:
5194:
5193:
5188:
5186:
5185:
5178:
5171:
5163:
5157:
5156:
5144:
5138:
5133:
5120:
5110:
5103:
5102:External links
5100:
5099:
5098:
5051:
5004:
4973:
4967:
4954:
4938:
4924:
4907:10.1.1.339.476
4875:
4828:
4810:(3): 166â170.
4799:
4750:
4747:
4746:
4745:
4739:
4727:O.D. Jefimenko
4723:
4717:
4705:O.D. Jefimenko
4701:
4695:
4682:
4676:
4660:
4654:
4641:
4635:
4622:
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4601:
4595:
4578:
4575:
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4570:
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4566:
4548:
4533:
4513:
4506:
4488:
4469:(3): 166â170.
4453:
4438:
4421:10.1.1.339.476
4384:
4363:
4310:
4296:
4242:
4226:
4214:
4173:
4158:
4105:
4092:10.1086/422304
4068:(2): 952â963.
4052:
4009:
3983:
3963:
3948:
3907:
3906:
3904:
3901:
3899:
3898:
3893:
3888:
3883:
3878:
3873:
3868:
3863:
3858:
3853:
3851:Frame-dragging
3848:
3843:
3837:
3835:
3832:
3811:do not form a
3808:
3801:
3789:
3788:
3739:
3737:
3730:
3724:
3721:
3713:
3712:
3698:
3693:
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3269:
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3205:
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3188:
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2533:
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2512:
2495:
2494:
2453:
2451:
2444:
2437:
2436:
2395:
2393:
2386:
2380:
2377:
2370:Coriolis field
2332:
2329:
2301:
2275:
2267:
2264:
2261:
2260:
2248:
2244:
2240:
2234:
2230:
2224:
2220:
2216:
2211:
2199:
2181:
2176:
2173:
2163:
2155:
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2143:
2139:
2133:
2130:
2119:
2105:
2104:
2101:
2087:
2084:
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2082:
2072:
2062:
2043:
2042:
2030:
2025:
2021:
2017:
2010:
2003:
1998:
1994:
1991:
1981:
1969:
1957:
1946:
1941:
1938:
1934:
1930:
1917:
1911:
1907:
1904:
1894:
1881:
1880:
1877:
1859:
1856:
1836:
1803:
1800:
1791:
1766:
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1760:
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1743:
1739:
1728:
1727:
1715:
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1613:
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1594:
1590:
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1575:
1562:
1558:
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1548:
1545:
1536:
1527:
1523:
1519:
1511:
1507:
1503:
1492:
1486:
1482:
1471:
1467:
1463:
1458:
1430:
1419:
1414:
1405:
1400:
1388:
1387:
1369:
1364:
1361:
1358:
1348:
1333:
1323:
1307:
1306:
1292:
1289:
1277:
1272:
1266:
1257:
1250:
1247:
1244:
1238:
1235:
1223:
1218:
1212:
1203:
1189:
1186:
1176:
1162:according to:
1144:
1116:
1103:
1100:
1099:
1098:
1095:speed of light
1084:
1077:
1072:
1063:
1054:
1046:
1039:
1033:
1026:
1015:
1010:
1008:charge density
1001:
993:
988:
986:magnetic field
979:
975:
970:
968:electric field
961:
953:
942:
941:
929:
920:
916:
910:
906:
901:
896:
890:
887:
881:
877:
867:
863:
859:
854:
850:
846:
843:
833:
815:
806:
802:
797:
794:
791:
785:
782:
776:
773:
761:
756:
746:
742:
738:
733:
723:
718:
715:
704:
703:
692:
689:
683:
680:
674:
670:
664:
660:
656:
653:
643:
632:
629:
623:
620:
608:
603:
597:
587:
582:
579:
568:
567:
553:
550:
546:
542:
539:
529:
515:
512:
502:
497:
494:
483:
482:
467:
463:
459:
454:
450:
446:
443:
433:
413:
409:
406:
403:
400:
397:
387:
382:
379:
368:
367:
364:
363:GEM equations
347:flat spacetime
345:or reasonably
322:
319:
315:
314:
302:
295:
293:
283:
276:
274:
256:magnetic field
248:
241:
239:
218:
211:
208:
207:
203:
202:
201:
158:frame-dragging
112:
109:
94:test particles
53:, abbreviated
32:frame-dragging
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5861:
5850:
5847:
5845:
5842:
5840:
5837:
5836:
5834:
5819:
5816:
5814:
5811:
5810:
5808:
5804:
5798:
5795:
5793:
5790:
5788:
5785:
5780:
5776:
5773:
5772:FatioâLe Sage
5769:
5768:
5767:
5764:
5762:
5759:
5757:
5754:
5752:
5749:
5748:
5746:
5744:
5738:Pre-Newtonian
5736:
5726:
5723:
5721:
5718:
5716:
5713:
5711:
5708:
5706:
5703:
5702:
5700:
5694:
5685:
5681:
5680:
5679:
5676:
5671:
5667:
5664:
5660:
5657:
5653:
5650:
5646:
5643:
5639:
5636:
5632:
5629:
5625:
5622:
5618:
5617:
5616:
5615:String theory
5613:
5608:
5604:
5603:
5602:
5599:
5597:
5594:
5592:
5589:
5588:
5586:
5580:
5574:
5571:
5569:
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5565:
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5548:
5545:
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5535:
5533:
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5525:
5521:
5518:
5514:
5511:
5507:
5506:
5505:
5502:
5500:
5497:
5496:
5494:
5490:
5484:
5481:
5479:
5476:
5474:
5471:
5469:
5466:
5461:
5457:
5456:
5455:
5452:
5450:
5447:
5445:
5442:
5437:
5433:
5432:
5431:
5428:
5426:
5423:
5418:
5414:
5411:
5407:
5406:
5405:
5402:
5400:
5397:
5395:
5392:
5390:
5388:
5384:
5380:
5378:
5375:
5373:
5370:
5368:
5365:
5360:
5356:
5353:
5349:
5348:
5347:
5344:
5343:
5341:
5337:
5331:
5328:
5326:
5323:
5321:
5318:
5317:
5315:
5311:
5308:
5306:
5300:
5290:
5287:
5285:
5284:ADM formalism
5282:
5280:
5277:
5275:
5272:
5270:
5267:
5265:
5262:
5260:
5257:
5255:
5252:
5250:
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5245:
5242:
5241:
5239:
5237:
5233:
5227:
5224:
5222:
5219:
5217:
5214:
5212:
5209:
5208:
5206:
5202:
5199:
5195:
5191:
5184:
5179:
5177:
5172:
5170:
5165:
5164:
5161:
5154:
5153:
5152:New Scientist
5148:
5145:
5142:
5139:
5137:
5134:
5131:
5127:
5124:
5121:
5118:
5114:
5111:
5109:
5106:
5105:
5101:
5095:
5091:
5087:
5083:
5079:
5075:
5070:
5065:
5061:
5057:
5052:
5048:
5044:
5040:
5036:
5032:
5028:
5023:
5022:gr-qc/0612140
5018:
5015:(2): 024021.
5014:
5010:
5005:
5001:
4997:
4992:
4991:gr-qc/0012091
4987:
4983:
4979:
4974:
4970:
4964:
4960:
4955:
4949:
4948:gr-qc/0311030
4944:
4939:
4935:
4931:
4927:
4921:
4917:
4913:
4908:
4903:
4899:
4895:
4890:
4889:gr-qc/0011014
4885:
4881:
4876:
4872:
4868:
4864:
4860:
4856:
4852:
4847:
4846:gr-qc/0106043
4842:
4838:
4834:
4829:
4825:
4821:
4817:
4813:
4809:
4805:
4800:
4796:
4792:
4788:
4784:
4780:
4776:
4771:
4770:gr-qc/0003115
4766:
4762:
4758:
4753:
4752:
4748:
4742:
4736:
4732:
4728:
4724:
4720:
4714:
4710:
4706:
4702:
4698:
4692:
4688:
4683:
4679:
4673:
4669:
4665:
4661:
4657:
4655:9780805387322
4651:
4647:
4642:
4638:
4636:9780805386622
4632:
4628:
4623:
4619:
4617:9780521845632
4613:
4609:
4608:
4602:
4598:
4596:9780521829519
4592:
4588:
4587:
4581:
4580:
4576:
4571:
4562:
4558:
4552:
4549:
4544:
4540:
4536:
4530:
4526:
4525:
4517:
4514:
4509:
4503:
4499:
4492:
4489:
4484:
4480:
4476:
4472:
4468:
4464:
4457:
4454:
4449:
4445:
4441:
4435:
4431:
4427:
4422:
4417:
4413:
4409:
4404:
4403:gr-qc/0011014
4399:
4395:
4388:
4385:
4379:
4378:gr-qc/0311030
4374:
4367:
4364:
4359:
4355:
4351:
4347:
4343:
4339:
4334:
4333:gr-qc/0003115
4329:
4325:
4321:
4314:
4311:
4307:
4303:
4299:
4293:
4289:
4285:
4280:
4275:
4271:
4267:
4262:
4261:gr-qc/9912027
4257:
4253:
4246:
4243:
4240:
4239:0-691-03323-4
4236:
4230:
4227:
4224:
4218:
4215:
4210:
4206:
4202:
4198:
4193:
4188:
4184:
4177:
4174:
4169:
4162:
4159:
4153:
4148:
4144:
4140:
4135:
4130:
4126:
4122:
4121:
4116:
4109:
4106:
4101:
4097:
4093:
4089:
4085:
4081:
4076:
4071:
4067:
4063:
4056:
4053:
4048:
4044:
4040:
4036:
4032:
4028:
4024:
4020:
4013:
4010:
4005:
4001:
3997:
3993:
3987:
3984:
3979:
3978:
3973:
3967:
3964:
3959:
3955:
3951:
3945:
3941:
3937:
3932:
3927:
3923:
3919:
3912:
3909:
3902:
3897:
3894:
3892:
3889:
3887:
3884:
3882:
3879:
3877:
3874:
3872:
3869:
3867:
3864:
3862:
3859:
3857:
3854:
3852:
3849:
3847:
3844:
3842:
3839:
3838:
3833:
3831:
3827:
3825:
3824:Lorentz boost
3820:
3818:
3814:
3807:
3800:
3796:
3785:
3782:
3774:
3764:
3760:
3756:
3750:
3749:
3745:
3740:This section
3738:
3734:
3729:
3728:
3722:
3720:
3718:
3696:
3691:
3687:
3683:
3680:
3675:
3672:
3669:
3666:
3660:
3651:
3643:
3642:
3641:
3639:
3631:
3629:
3627:
3622:
3621:
3616:
3615:
3595:
3593:
3573:
3569:
3565:
3560:
3557:
3554:
3531:
3525:
3520:
3516:
3512:
3507:
3504:
3501:
3498:
3492:
3487:
3483:
3480:
3472:
3469:
3459:
3455:
3451:
3447:
3442:
3433:
3425:
3424:
3423:
3421:
3417:
3409:
3407:
3405:
3387:
3380:
3376:
3360:
3356:
3352:
3348:
3343:
3324:
3323:
3322:
3320:
3316:
3312:
3308:
3304:
3302:
3297:
3278:
3271:
3267:
3262:
3258:
3246:
3242:
3233:
3222:
3219:
3203:
3199:
3195:
3191:
3186:
3171:
3165:
3146:
3145:
3144:
3139:
3131:
3128:
3125:
3121:
3118:
3115:
3111:
3108:
3105:
3086:
3079:
3076:
3072:
3054:
3048:
3044:
3040:
3037:
3031:
3022:
3014:
3011:
2986:
2985:
2984:
2964:
2960:
2957:
2949:
2943:
2939:
2935:
2932:
2926:
2923:
2914:
2910:
2907:
2896:
2890:
2886:
2882:
2877:
2874:
2869:
2850:
2846:
2836:
2820:
2816:
2812:
2808:
2803:
2800:
2781:
2780:
2779:
2728:
2724:
2718:
2714:
2706:
2702:
2697:
2694:
2691:
2685:
2682:
2665:
2653:
2652:
2651:
2650:. Therefore
2632:
2628:
2624:
2598:
2567:
2563:
2555:
2551:
2546:
2543:
2540:
2534:
2531:
2514:
2502:
2501:
2500:
2491:
2488:
2480:
2477:February 2024
2470:
2466:
2460:
2459:
2454:This section
2452:
2448:
2443:
2442:
2433:
2430:
2422:
2412:
2408:
2402:
2401:
2394:
2385:
2384:
2378:
2376:
2373:
2371:
2367:
2362:
2356:
2354:
2350:
2346:
2342:
2337:
2330:
2328:
2326:
2325:
2320:
2316:
2312:
2308:
2300:
2292:
2274:
2265:
2242:
2232:
2228:
2222:
2218:
2214:
2200:
2174:
2171:
2153:
2150:
2147:
2141:
2137:
2131:
2128:
2107:
2106:
2102:
2100:GEM equation
2099:
2098:
2095:
2094:is given by:
2093:
2085:
2080:
2076:
2073:
2070:
2066:
2063:
2061:
2060:test particle
2057:
2053:
2050:
2049:
2048:
2028:
2019:
2008:
1996:
1992:
1989:
1970:
1955:
1939:
1936:
1928:
1909:
1905:
1902:
1883:
1882:
1878:
1876:GEM equation
1875:
1874:
1871:
1869:
1868:Lorentz force
1865:
1858:Lorentz force
1857:
1855:
1823:
1821:
1817:
1816:wave equation
1801:
1798:
1789:
1780:
1764:
1761:
1758:
1751:
1741:
1707:
1703:
1695:
1691:
1686:
1683:
1680:
1674:
1654:
1646:
1638:
1634:
1611:
1596:
1592:
1588:
1583:
1576:
1560:
1556:
1552:
1549:
1546:
1543:
1534:
1525:
1517:
1509:
1505:
1490:
1484:
1469:
1465:
1461:
1456:
1449:
1448:
1447:
1445:
1428:
1412:
1403:
1398:
1362:
1356:
1331:
1312:
1311:
1310:
1290:
1264:
1255:
1245:
1242:
1236:
1210:
1201:
1187:
1184:
1165:
1164:
1163:
1114:
1101:
1096:
1092:
1088:
1085:
1083:
1076:
1073:
1071:
1067:
1064:
1062:
1058:
1055:
1052:
1045:
1038:
1032:
1025:
1021:
1014:
1011:
1009:
1005:
1002:
999:
992:
989:
987:
983:
980:
974:
971:
969:
965:
962:
959:
952:
949:
948:
947:
918:
914:
908:
904:
899:
894:
888:
865:
861:
857:
852:
844:
834:
804:
800:
795:
792:
789:
783:
780:
774:
744:
740:
736:
731:
716:
706:
705:
690:
687:
681:
662:
654:
644:
630:
627:
621:
595:
580:
570:
569:
551:
548:
540:
530:
513:
510:
495:
485:
484:
465:
461:
457:
452:
444:
434:
411:
407:
404:
401:
398:
395:
380:
370:
369:
365:
362:
361:
358:
356:
352:
348:
344:
340:
336:
332:
328:
325:According to
320:
311:
308:â rotational
307:
306:
299:
294:
287:
280:
275:
270:
266:
265:dipole moment
261:
257:
253:
252:
245:
240:
235:
231:
226:
221:
215:
210:
200:
198:
194:
190:
185:
183:
179:
175:
171:
167:
163:
159:
155:
154:Roger Penrose
151:
146:
143:
139:
135:
130:
126:
122:
118:
110:
108:
106:
102:
97:
95:
91:
87:
83:
79:
75:
71:
68:
64:
60:
56:
52:
46:
41:
37:
33:
19:
5740:theories and
5573:Supergravity
5386:
5382:
5244:Introduction
5150:
5059:
5055:
5012:
5008:
4981:
4977:
4958:
4879:
4836:
4832:
4807:
4803:
4760:
4756:
4730:
4708:
4686:
4667:
4664:J.A. Wheeler
4645:
4626:
4606:
4585:
4560:
4551:
4523:
4516:
4497:
4491:
4466:
4462:
4456:
4393:
4387:
4366:
4323:
4319:
4313:
4251:
4245:
4229:
4217:
4182:
4176:
4167:
4161:
4124:
4118:
4108:
4065:
4061:
4055:
4022:
4018:
4012:
3995:
3986:
3976:
3972:O. Heaviside
3966:
3921:
3911:
3841:Anti-gravity
3828:
3821:
3805:
3798:
3792:
3777:
3768:
3753:Please help
3741:
3714:
3635:
3619:
3613:
3596:
3546:
3413:
3402:
3314:
3310:
3306:
3300:
3293:
3137:
3135:
3129:
3119:
3109:
2982:
2748:
2589:
2498:
2483:
2474:
2463:Please help
2458:verification
2455:
2425:
2416:
2397:
2374:
2365:
2357:
2338:
2334:
2322:
2317:to electric
2311:four-current
2298:
2290:
2272:
2269:
2103:EM equation
2089:
2074:
2064:
2051:
2046:
1879:EM equation
1863:
1861:
1824:
1729:
1444:Lorenz gauge
1389:
1308:
1105:
1089:is both the
1086:
1074:
1065:
1059:is electric
1056:
1043:
1036:
1030:
1023:
1012:
1003:
998:mass density
990:
981:
972:
963:
950:
945:
324:
303:
268:
259:
249:
233:
224:
219:
186:
147:
141:
137:
133:
114:
98:
85:
67:relativistic
54:
50:
49:
36:
5542:Causal sets
5436:BransâDicke
5254:Mathematics
4984:: 459â461.
4839:(1): 1â50.
3924:: 215â220.
3813:four-vector
3319:dot product
187:A group at
162:black holes
117:gravitation
70:gravitation
5833:Categories
5756:CGHS model
5743:toy models
5119:) research
5069:1610.09819
4561:google.com
4134:2006.13287
3992:R. Penrose
3931:1512.05183
3903:References
3603:10 Hz
2349:smoke ring
2345:minor axis
1870:equation:
1102:Potentials
310:fluid drag
111:Background
5761:RST model
5547:DGP model
5524:Spin foam
5468:Whitehead
5460:Nordström
5389:) gravity
5339:Classical
5313:Paradigms
5264:Resources
5094:119232668
5062:(3): 44.
4934:263798773
4902:CiteSeerX
4543:904397831
4448:263798773
4416:CiteSeerX
4274:CiteSeerX
3958:118596433
3771:July 2024
3742:does not
3670:π
3628:mission.
3502:π
3484:π
3234:⋅
3220:−
3172:×
3169:∇
3087:ω
2961:π
2924:ω
2897:ω
2837:×
2804:−
2729:×
2725:ω
2715:ρ
2695:π
2686:−
2662:∇
2633:×
2629:ω
2599:ω
2564:ρ
2544:π
2535:−
2511:∇
2407:talk page
2243:×
2229:ε
2172:×
2151:π
2132:−
2020:×
1937:×
1790:ρ
1756:∂
1742:ϕ
1738:∂
1704:ρ
1684:π
1651:∇
1631:∂
1608:∂
1584:−
1557:ρ
1550:π
1535:ϕ
1522:∇
1502:∂
1491:ϕ
1481:∂
1457:−
1404:ϕ
1363:×
1360:∇
1288:∂
1271:∂
1265:−
1256:ϕ
1249:∇
1246:−
1234:∂
1217:∂
1211:−
1202:ϕ
1188:−
1115:ϕ
1020:mass flux
905:ϵ
886:∂
876:∂
853:−
845:×
842:∇
793:π
784:−
772:∂
755:∂
732:−
717:×
714:∇
679:∂
669:∂
655:×
652:∇
619:∂
602:∂
581:×
578:∇
541:⋅
538:∇
496:⋅
493:∇
462:ϵ
458:ρ
445:⋅
442:∇
412:ρ
405:π
399:−
381:⋅
378:∇
321:Equations
263:due to a
5818:Graviton
5628:F-theory
5621:M-theory
5197:Standard
5126:Archived
5047:14846902
4795:15724290
4729:(2006).
4707:(1992).
4689:. Nova.
4358:15724290
4306:32411999
4047:10018300
3974:(1893).
3834:See also
3611:10
3438:g, Earth
2419:May 2013
2400:disputed
2353:g-forces
2341:toroidal
2056:velocity
1093:and the
1051:velocity
1042:, where
90:magnetic
5249:History
5074:Bibcode
5027:Bibcode
4996:Bibcode
4894:Bibcode
4871:6691986
4851:Bibcode
4812:Bibcode
4775:Bibcode
4471:Bibcode
4408:Bibcode
4338:Bibcode
4266:Bibcode
4197:Bibcode
4139:Bibcode
4100:1350543
4080:Bibcode
4027:Bibcode
4000:Bibcode
3763:removed
3748:sources
3420:equator
3303:-factor
3122:is the
3112:is the
3102:is the
3069:is the
3012:vector;
3008:is the
2983:where:
2295:
2280:
2077:is the
2067:is the
2058:of the
2054:is the
2047:where:
1080:is the
1068:is the
1049:is the
984:is the
966:is the
946:where:
286:current
178:quasars
123:in the
5092:
5045:
4965:
4932:
4922:
4904:
4869:
4793:
4749:Papers
4737:
4715:
4693:
4674:
4652:
4633:
4614:
4593:
4541:
4531:
4504:
4446:
4436:
4418:
4356:
4304:
4294:
4276:
4237:
4098:
4045:
3956:
3946:
3799:ρ
3632:Pulsar
3547:where
3124:radius
3090:
2361:chiral
2012:
2006:
1926:
1777:) the
1660:
1531:
1342:
1252:
1198:
555:
517:
421:
329:, the
5410:AQUAL
5269:Tests
5090:S2CID
5064:arXiv
5043:S2CID
5017:arXiv
4986:arXiv
4943:arXiv
4930:S2CID
4884:arXiv
4867:S2CID
4841:arXiv
4791:S2CID
4765:arXiv
4577:Books
4444:S2CID
4398:arXiv
4373:arXiv
4354:S2CID
4328:arXiv
4302:S2CID
4256:arXiv
4187:arXiv
4129:arXiv
4096:S2CID
4070:arXiv
3954:S2CID
3926:arXiv
3605:, or
3599:1.012
3416:Earth
3410:Earth
136:and
4963:ISBN
4920:ISBN
4735:ISBN
4713:ISBN
4691:ISBN
4672:ISBN
4650:ISBN
4631:ISBN
4612:ISBN
4591:ISBN
4539:OCLC
4529:ISBN
4502:ISBN
4434:ISBN
4292:ISBN
4235:ISBN
4043:PMID
3944:ISBN
3804:and
3746:any
3744:cite
3422:is:
3313:and
3114:mass
3027:ball
2919:ball
2860:with
2366:both
2297:and
2069:mass
1814:) a
1309:and
1193:grad
353:for
180:and
80:for
65:and
5117:esa
5082:doi
5035:doi
4912:doi
4859:doi
4837:215
4820:doi
4783:doi
4479:doi
4426:doi
4346:doi
4284:doi
4205:doi
4147:doi
4088:doi
4066:611
4035:doi
3936:doi
3757:by
3607:3.1
3590:is
2467:by
1337:rot
1006:is
996:is
272:...
55:GEM
5835::
5149:,
5088:.
5080:.
5072:.
5060:49
5058:.
5041:.
5033:.
5025:.
5013:78
5011:.
4994:.
4982:75
4980:.
4953:in
4928:.
4918:.
4910:.
4900:.
4892:.
4865:.
4857:.
4849:.
4835:.
4818:.
4808:31
4806:.
4789:.
4781:.
4773:.
4761:17
4759:.
4559:.
4537:.
4477:.
4467:31
4465:.
4442:.
4432:.
4424:.
4414:.
4406:.
4352:.
4344:.
4336:.
4324:17
4322:.
4300:,
4290:,
4282:,
4272:,
4264:,
4203:.
4195:.
4145:.
4137:.
4125:29
4123:.
4117:.
4094:.
4086:.
4078:.
4064:.
4041:.
4033:.
4023:51
4021:.
3952:.
3942:.
3934:.
3920:.
3077:);
2903:or
2355:.
1332::=
1185::=
1029:=
254:â
164:.
152:.
107:.
96:.
84:.
5387:R
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