213:). It is derived by rewriting the Einstein–Hilbert action in terms of the affine connection and then separately posing a constraint that forces both the torsion and contorsion to be zero, which thus forces the affine connection to be equal to the Levi-Civita connection. Because it is a direct translation of the action and field equations of general relativity, expressed in terms of the Levi-Civita connection, this may be regarded as the theory of general relativity, itself, transposed into the framework of Riemann–Cartan geometry.
4474:
33:
4018:
1451:, and vanishes outside of matter. Therefore, in principle the torsion can be algebraically eliminated from the theory in favor of the spin tensor, which generates an effective "spin–spin" nonlinear self-interaction inside matter. Torsion is equal to its source term and can be replaced by a boundary or a topological structure with a throat such as a "wormhole".
151:
by first reformulating general relativity onto a
Riemann–Cartan geometry, replacing the Einstein–Hilbert action over Riemannian geometry by the Palatini action over Riemann–Cartan geometry; and second, removing the zero torsion constraint from the Palatini action, which results in the additional set
248:
A consequence of the linearity is that outside of matter there is zero torsion, so that the exterior geometry remains the same as what would be described in general relativity. The differences between
Einstein–Cartan theory and general relativity (formulated either in terms of the Einstein–Hilbert
252:
Because
Riemann–Cartan geometries have Lorentz symmetry as a local gauge symmetry, it is possible to formulate the associated conservation laws. In particular, regarding the metric and torsion tensors as independent variables gives the correct generalization of the conservation law for the total
249:
action on
Riemannian geometry or the Palatini action on Riemann–Cartan geometry) rest solely on what happens to the geometry inside matter sources. That is: "torsion does not propagate". Generalizations of the Einstein–Cartan action have been considered which allow for propagating torsion.
224:(1) the field equations are now expressed in terms of affine connection, rather than the Levi-Civita connection, and so have additional terms in Einstein's field equations involving the contorsion that are not present in the field equations derived from the Palatini formulation;
1226:
1522:
in quantum field theory. According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular black hole. In the
Einstein–Cartan theory, instead, the collapse reaches a bounce and forms a regular Einstein–Rosen bridge
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1388:
862:
493:
127:(1) it is formulated within the framework of Riemann–Cartan geometry, which possesses a locally gauged Lorentz symmetry, while general relativity is formulated within the framework of Riemannian geometry, which does not;
331:
to be the true action of spacetime and then varying that action with respect to the metric tensor. The field equations of
Einstein–Cartan theory come from exactly the same approach, except that a general asymmetric
307:"never understood what is so important physically about the possibility of torsion in differential geometry", other physicists claim that theories with torsion are valuable. The theory has indirectly influenced
294:
because torsion seemed to add little predictive benefit at the expense of the tractability of its equations. Since the
Einstein–Cartan theory is purely classical, it also does not fully address the issue of
947:
205:
Because the contorsion can be expressed linearly in terms of the torsion, then is also possible to directly translate the
Einstein–Hilbert action into a Riemann–Cartan geometry, the result being the
1027:. The Ricci tensor is no longer symmetric because the connection contains a nonzero torsion tensor; therefore, the right-hand side of the equation cannot be symmetric either, implying that
1121:
415:
378:
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245:). These extra equations express the torsion linearly in terms of the spin tensor associated with the matter source, which entails that the torsion generally be non-zero inside matter.
1506:
was contracting. This scenario also explains why the present
Universe at largest scales appears spatially flat, homogeneous and isotropic, providing a physical alternative to cosmic
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1434:
179:
in curved spacetime geometries. The result of adding this infrastructure is a
Riemann–Cartan geometry. In particular, to be able to describe spinors requires the inclusion of a
4414:
499:
2267:
Cabral, F.; Lobo, F.S.N.; Rubiera-Garcia, D. (2020). "Cosmological bounces, cyclic universes, and effective cosmological constant in Einstein-Cartan-Dirac-Maxwell theory".
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1066:
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Einstein–Cartan theory relaxes this condition and, correspondingly, relaxes general relativity's assumption that the affine connection have a vanishing antisymmetric part (
4000:
1109:
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775:
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represent the Lagrangian density of the gravitational field. The Lagrangian density for the gravitational field in the Einstein–Cartan theory is proportional to the
220:). The action used is the same as the Palatini action, except that the constraint on the torsion is removed. This results in two differences from general relativity:
1055:
1018:
984:
767:
4025:
3467:
1976:
Hehl, Friedrich W.; von der Heyde, Paul; Kerlick, G. David; Nester, James M. (1976-07-01). "General relativity with spin and torsion: Foundations and prospects".
702:
605:
2729:
Hehl, Friedrich W.; von der Heyde, Paul; Kerlick, G. David (1974-08-15). "General relativity with spin and torsion and its deviations from Einstein's theory".
1486:) need not hold in Riemann–Cartan geometry. Consequently, Einstein–Cartan theory is able to avoid the general-relativistic problem of the singularity at the
3945:
3273:
4419:
1490:. The minimal coupling between torsion and Dirac spinors generates an effective nonlinear spin–spin self-interaction, which becomes significant inside
427:
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3195:
167:. At the time of its original formulation, there was no concept of Riemann–Cartan geometry. Nor was there a sufficient awareness of the concept of
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175:, such as would be required to be able to express continuity equations and conservation laws for rotational and boost symmetries, or to describe
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108:
1531:; pair production by the gravitational field after the bounce, when torsion is still strong, generates a finite period of inflation.
56:
43:
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3238:
75:
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2766:
Kleinert, Hagen (2000). "Nonholonomic Mapping Principle for Classical and Quantum Mechanics in Spaces with Curvature and Torsion".
152:
of equations for spin and torsion, as well as the addition of extra spin-related terms in the Einstein field equations themselves.
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matter at extremely high densities. Such an interaction is conjectured to replace the singular Big Bang with a cusp-like
1444:
3930:
3925:
4500:
4041:
2197:
N. Popławski (2023). "Chapter 13: Gravitational Collapse with Torsion and Universe in a Black Hole". In C. Bambi (ed.).
270:
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328:
160:
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3378:
3253:
1221:{\displaystyle {\frac {\delta {\mathcal {L}}_{\mathrm {G} }}{\delta {T^{ab}}_{c}}}-{\frac {1}{2}}{\sigma _{ab}}^{c}=0}
290:
Einstein–Cartan theory has been historically overshadowed by its torsion-free counterpart and other alternatives like
4101:
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387:
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233:) of matter, much in the same way in which the affine connection is coupled to the energy and momentum of matter.
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1021:
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4049:
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3585:
2027:
Hehl, F. W.; Datta, B. K. (1971). "Nonlinear Spinor Equation and Asymmetric Connection in General Relativity".
1499:
341:
229:(2) an additional set of equations are now present which couple the torsion to the intrinsic angular momentum (
164:
4429:
3552:
2111:
Ellis, George F. R.; Penrose, Sir Roger (2010). "Dennis William Sciama. 18 November 1926 — 19 December 1999".
4434:
3619:
681:
324:
3420:
3330:
1743:"Sur les variétés à connexion affine, et la théorie de la relativité généralisée (première partie) (Suite)"
291:
171:
to understand that Riemannian geometries do not possess the requisite structure to embody a locally gauged
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Singularity theorems which are premised on and formulated within the setting of Riemannian geometry (e.g.
673:
337:
191:
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The chief difference between a Riemann–Cartan geometry and Riemannian geometry is that in the former, the
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1400:
577:{\displaystyle S=\int \left({\mathcal {L}}_{\mathrm {G} }+{\mathcal {L}}_{\mathrm {M} }\right)\,d^{4}x,}
273:
as part of a unified field theory. This line of thought led him to the related but different theory of
3205:
1383:{\displaystyle {T_{ab}}^{c}+{g_{a}}^{c}{T_{bd}}^{d}-{g_{b}}^{c}{T_{ad}}^{d}=\kappa {\sigma _{ab}}^{c}}
4318:
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1985:
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857:{\displaystyle {\frac {\delta {\mathcal {L}}_{\mathrm {G} }}{\delta g^{ab}}}-{\frac {1}{2}}P_{ab}=0}
1784:"Sur les variétés à connexion affine, et la théorie de la relativité généralisée (deuxième partie)"
1503:
1437:
156:
92:
1702:"Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie)"
1075:
634:
269:
became affiliated with the theory in 1928 during his unsuccessful attempt to match torsion to the
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2009:
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381:
210:
4141:
2353:
Popławski, Nikodem J. (2012). "Nonsingular, big-bounce cosmology from spinor–torsion coupling".
287:
independently revisited the theory in the 1960s, and an important review was published in 1976.
2684:
Hehl, F. W. (1974). "Spin and torsion in general relativity II: Geometry and field equations".
202:) is zero for Levi-Civita connections, as one of the defining conditions for such connections.
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de Sabbata, V. and Sivaram, C. (1994). "Spin and Torsion in Gravitation" (World Scientific).
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2611:
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Popławski, Nikodem J. (2010). "Cosmology with torsion: An alternative to cosmic inflation".
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1993:
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993:
959:
742:
172:
2230:
K. Atazadeh (2014). "Stability of the Einstein static universe in Einstein-Cartan theory".
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3309:
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de Sabbata, V. and Gasperini, M. (1985). "Introduction to Gravitation" (World Scientific).
1678:
1472:
1112:
304:
296:
274:
266:
206:
4300:
2914:
Petti, R J (2006-01-12). "Translational spacetime symmetries in gravitational theories".
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1989:
1938:
1895:
1840:
1647:
1602:
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3895:
3662:
2821:
Kuchowicz, Bronisław (1978). "Friedmann-like cosmological models without singularity".
2408:
Popławski, Nikodem J. (2010). "Nonsingular Dirac particles in spacetime with torsion".
1859:
1824:
1511:
687:
677:
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312:
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217:
199:
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is independent of the metric, while in the latter it is derived from the metric as the
180:
168:
112:
17:
3068:
253:(orbital plus intrinsic) angular momentum to the presence of the gravitational field.
4494:
4336:
4306:
4193:
3599:
3268:
3084:
3008:
2969:
Petti, R. J. (2021). "Derivation of Einstein–Cartan theory from general relativity".
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2721:
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2631:
2615:
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2500:
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2456:
2394:
2183:
1679:"Sur une généralisation de la notion de courbure de Riemann et les espaces à torsion"
1611:
1576:
1528:
280:
230:
3092:
Trautman, Andrzej (1973). "Spin and Torsion May Avert Gravitational Singularities".
2813:
2132:
2013:
1962:
1634:
Neville, Donald E. (15 February 1980). "Gravity theories with propagating torsion".
4444:
4324:
3557:
3366:
2441:
2339:
1476:
987:
418:
2869:
Petti, R. J. (1976). "Some aspects of the geometry of first-quantized theories".
2216:
1575:
Cabral, Francisco; Lobo, Francisco S. N.; Rubiera-Garcia, Diego (December 2019).
488:{\displaystyle {\mathcal {L}}_{\mathrm {G} }={\frac {1}{2\kappa }}R{\sqrt {|g|}}}
4449:
4133:
3955:
3526:
2292:
1515:
1058:
608:
242:
2552:
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1057:
must include an asymmetric contribution that can be shown to be related to the
4454:
3740:
3000:
2797:
2639:
Hehl, F. W. (1973). "Spin and torsion in general relativity: I. Foundations".
1997:
1903:
1495:
284:
198:. In particular, the antisymmetric part of the connection (referred to as the
3121:
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2953:
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2758:
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2623:
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2005:
1954:
1911:
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1727:
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155:
The theory of general relativity was originally formulated in the setting of
3745:
3727:
3531:
3508:
1882:
Sciama, D. W. (1964-01-01). "The Physical Structure of General Relativity".
1655:
3113:
2124:
1925:
Kibble, T. W. B. (1961). "Lorentz Invariance and the Gravitational Field".
1868:
3143:
3802:
3612:
3605:
1524:
1487:
1061:. This canonical energy–momentum tensor is related to the more familiar
132:(2) an additional set of equations are posed that relate torsion to spin.
1849:
142:
general relativity (Einstein–Hilbert) → general relativity (Palatini) →
3174:
3051:
2890:
2842:
2705:
2660:
2167:
1800:
1783:
1759:
1742:
1718:
1701:
1491:
176:
3135:
2865:
Lord, E. A. (1976). "Tensors, Relativity and Cosmology" (McGraw-Hill).
2780:
2585:
2096:
2071:
2048:
1946:
2579:
Gronwald, F.; Hehl, F. W. (1996). "On the Gauge Aspects of Gravity".
2199:
Regular Black Holes: Towards a New Paradigm of Gravitational Collapse
2146:
Richard J. Petti (1986). "On the local geometry of rotating matter".
3037:
Shapiro, I.L. (2002). "Physical aspects of the space–time torsion".
1459:
Recently, interest in Einstein–Cartan theory has been driven toward
123:
Einstein–Cartan theory differs from general relativity in two ways:
2928:
2534:
2283:
2207:
1593:
3813:
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3022:
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2424:
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1448:
237:
In Einstein–Cartan theory, the torsion is now a variable in the
3817:
3147:
241:
that is coupled to a curved spacetime formulation of spin (the
1514:, which helps to avoid the formation of singularities such as
1510:. Torsion allows fermions to be spatially extended instead of
26:
344:), and then the metric and torsion are varied independently.
2971:
International Journal of Geometric Methods in Modern Physics
1134:
788:
539:
520:
434:
394:
357:
340:(i.e., spacetime is assumed to have torsion in addition to
303:
becomes nonlinear. Even though renowned physicists such as
1577:"Einstein–Cartan–Dirac gravity with U(1) symmetry breaking"
942:{\displaystyle R_{ab}-{\frac {1}{2}}Rg_{ab}=\kappa P_{ab}}
194:, the difference between the two being referred to as the
327:
of general relativity can be derived by postulating the
1436:
is the spin tensor. Because the torsion equation is an
51:
3016:
Poplawski, Nikodem J. (2009). "Spacetime and fields".
2516:"Big Bounce and closed universe from spin and torsion"
1527:) to a new, growing universe on the other side of the
4086:
Die Grundlagen der Einsteinschen Relativitäts-Theorie
2457:"Universe in a black hole in Einstein-Cartan gravity"
1403:
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690:
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430:
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353:
3129:
Trautman, Andrzej (2006). "Einstein–Cartan Theory".
2594:
Hammond, Richard T (2002-03-27). "Torsion gravity".
2113:
Biographical Memoirs of Fellows of the Royal Society
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Annales Scientifiques de l'École Normale Supérieure
1747:
Annales Scientifiques de l'École Normale Supérieure
1706:
Annales Scientifiques de l'École Normale Supérieure
1463:implications, most importantly, the avoidance of a
1683:Comptes rendus de l'Académie des Sciences de Paris
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978:
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409:
372:
265:in 1922 and expounded in the following few years.
4019:Investigations on the Theory of Brownian Movement
1467:at the beginning of the universe, such as in the
1072:The variation with respect to the torsion tensor
704:for the gravitational field and matter vanishes:
739:The variation with respect to the metric tensor
4026:Relativity: The Special and the General Theory
3468:Degenerate Higher-Order Scalar-Tensor theories
2232:Journal of Cosmology and Astroparticle Physics
3829:
3159:
410:{\displaystyle {\mathcal {L}}_{\mathrm {G} }}
373:{\displaystyle {\mathcal {L}}_{\mathrm {M} }}
183:, which suffices to produce such a geometry.
60:that contextualizes different points of view.
46:to certain ideas, incidents, or controversies
8:
1447:, the torsion field does not propagate as a
3836:
3822:
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3294:
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1825:"On the History of Unified Field Theories"
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76:Learn how and when to remove this message
4460:Emergency Committee of Atomic Scientists
1232:
868:
3772:Gravitational interaction of antimatter
1567:
4204:Albert Einstein World Award of Science
299:. In the Einstein–Cartan theory, the
3777:Physics in the medieval Islamic world
3700:(2+1)-dimensional topological gravity
3196:Newton's law of universal gravitation
336:is assumed rather than the symmetric
136:This difference can be factored into
7:
3522:Asymptotic safety in quantum gravity
1484:Penrose–Hawking singularity theorems
684:, the variation of the total action
101:Einstein–Cartan–Sciama–Kibble theory
311:(and seems also to have influenced
111:. The theory was first proposed by
4233:Albert Einstein: Creator and Rebel
3946:Einstein–Infeld–Hoffmann equations
3916:Einstein relation (kinetic theory)
3274:Gibbons–Hawking–York boundary term
2871:General Relativity and Gravitation
2823:General Relativity and Gravitation
2768:General Relativity and Gravitation
2686:General Relativity and Gravitation
2641:General Relativity and Gravitation
2148:General Relativity and Gravitation
1541:Alternatives to general relativity
1429:{\displaystyle {\sigma _{ab}}^{c}}
1141:
795:
546:
527:
441:
401:
364:
109:alternatives to general relativity
25:
4094:The Einstein Theory of Relativity
3389:Modified Newtonian dynamics, MOND
3305:Classical theories of gravitation
2514:Unger, G.; Popławski, N. (2019).
261:The theory was first proposed by
4473:
4472:
4209:Einstein Prize for Laser Science
1546:Metric-affine gravitation theory
31:
4254:Einstein: His Life and Universe
3211:History of gravitational theory
2029:Journal of Mathematical Physics
1927:Journal of Mathematical Physics
1581:The European Physical Journal C
769:yields the Einstein equations:
105:classical theory of gravitation
88:Classical theory of gravitation
3876:Mass–energy equivalence (E=mc)
3517:Causal dynamical triangulation
3206:Poisson's equation for gravity
2596:Reports on Progress in Physics
2442:10.1016/j.physletb.2010.04.073
2340:10.1016/j.physletb.2010.09.056
2201:. Springer. pp. 485–499.
1823:Goenner, Hubert F. M. (2004).
1612:10.1140/epjc/s10052-019-7536-3
1067:Belinfante–Rosenfeld procedure
1065:energy–momentum tensor by the
479:
471:
239:principle of stationary action
1:
3069:10.1016/s0370-1573(01)00030-8
2916:Classical and Quantum Gravity
2254:10.1088/1475-7516/2014/06/020
1445:partial differential equation
1025:stress–energy–momentum tensor
2217:10.1007/978-981-99-1596-5_13
2072:"Note on the torsion tensor"
1829:Living Reviews in Relativity
1104:{\displaystyle {T^{ab}}_{c}}
665:{\displaystyle 8\pi G/c^{4}}
271:electromagnetic field tensor
4199:Albert Einstein Peace Prize
3976:Unsuccessful investigations
3379:Infinite derivative gravity
2293:10.1103/PhysRevD.102.083509
2070:Hehl, Friedrich W. (2007).
729:{\displaystyle \delta S=0.}
4522:
4126:Picasso at the Lapin Agile
4064:Russell–Einstein Manifesto
3936:Bose–Einstein correlations
3567:Unified-field-theoric and
2946:10.1088/0264-9381/23/3/012
2616:10.1088/0034-4885/65/5/201
2492:10.3847/0004-637X/832/2/96
2387:10.1103/PhysRevD.85.107502
1455:Avoidance of singularities
611:of the metric tensor, and
4468:
4034:The Meaning of Relativity
3710:Jackiw–Teitelboim gravity
3489:Canonical quantum gravity
3484:Euclidean quantum gravity
3001:10.1142/S0219887821500833
1998:10.1103/revmodphys.48.393
1978:Reviews of Modern Physics
1904:10.1103/revmodphys.36.463
1884:Reviews of Modern Physics
1465:gravitational singularity
163:, out of which arise the
4425:Albert Einstein Archives
4355:Bernhard Caesar Einstein
4102:Relics: Einstein's Brain
4050:The Evolution of Physics
3931:Bose–Einstein statistics
3926:Bose–Einstein condensate
3906:Einstein field equations
3586:Superfluid vacuum theory
3410:Nonsymmetric gravitation
3259:Post-Newtonian formalism
2751:10.1103/physrevd.10.1066
2553:10.3847/1538-4357/aaf169
1498:at a minimum but finite
325:Einstein field equations
165:Einstein field equations
4435:Einstein Papers Project
3951:Einstein–de Haas effect
3751:Mechanical explanations
3620:Heterotic string theory
3576:Noncommutative geometry
3495:Wheeler–DeWitt equation
3221:General relativity (GR)
3201:Gauss's law for gravity
3175:Theories of gravitation
3094:Nature Physical Science
2798:10.1023/a:1001962922592
1656:10.1103/physrevd.21.867
631:is a physical constant
624:{\displaystyle \kappa }
329:Einstein–Hilbert action
161:Einstein–Hilbert action
18:Einstein-Cartan gravity
4367:Thomas Martin Einstein
4275:Introducing Relativity
4247:Einstein for Beginners
4150:Einstein and Eddington
3941:Einstein–Cartan theory
3592:Logarithmic BEC vacuum
3537:Rainbow gravity theory
3415:Scalar–tensor theories
3189:Newtonian gravity (NG)
3114:10.1038/physci242007a0
2977:(6): 2150083–2151205.
2455:Popławski, N. (2016).
2125:10.1098/rsbm.2009.0023
1520:ultraviolet divergence
1430:
1384:
1222:
1105:
1051:
1050:{\displaystyle P_{ab}}
1014:
1013:{\displaystyle P_{ab}}
980:
979:{\displaystyle R_{ab}}
943:
858:
763:
762:{\displaystyle g^{ab}}
730:
698:
674:gravitational constant
666:
625:
601:
578:
489:
411:
374:
338:Levi-Civita connection
192:Levi-Civita connection
97:Einstein–Cartan theory
4440:Einstein refrigerator
4430:Einstein's Blackboard
4309:(second wife; cousin)
4240:Einstein and Religion
4189:Albert Einstein Medal
4184:Albert Einstein Award
4042:The World as I See It
3981:Wave–particle duality
3961:Bohr–Einstein debates
3921:Cosmological constant
3901:Equivalence principle
3891:Einstein coefficients
3669:Twistor string theory
3648:Type II string theory
3641:Bosonic string theory
3581:Semiclassical gravity
3546:Unified-field-theoric
3331:Poincaré gauge theory
2521:Astrophysical Journal
2461:Astrophysical Journal
1782:Cartan, Elie (1925).
1741:Cartan, Elie (1924).
1700:Cartan, Elie (1923).
1431:
1385:
1223:
1106:
1052:
1015:
981:
944:
859:
764:
731:
699:
667:
626:
602:
579:
490:
412:
375:
54:by rewriting it in a
4319:Hans Albert Einstein
4268:I Am Albert Einstein
4214:Einstein Prize (APS)
3886:Photoelectric effect
3859:Theory of relativity
3736:Aristotelian physics
3705:Gauss–Bonnet gravity
3655:Little string theory
3634:Type 0 string theory
3627:Type I string theory
3502:Loop quantum gravity
3429:Scalar–tensor–vector
3402:Tensor–vector–scalar
3357:Gauge theory gravity
3315:Theory of everything
1677:Élie Cartan (1922).
1556:Loop quantum gravity
1551:Gauge theory gravity
1469:black hole cosmology
1401:
1239:
1122:
1076:
1031:
994:
960:
875:
776:
743:
711:
688:
682:Hamilton's principle
635:
615:
591:
500:
428:
388:
351:
309:loop quantum gravity
99:, also known as the
4501:Theories of gravity
3971:Thought experiments
3553:Kaluza–Klein theory
3106:1973NPhS..242....7T
3061:2002PhR...357..113S
2993:2021IJGMM..1850083P
2938:2006CQGra..23..737P
2883:1976GReGr...7..869P
2835:1978GReGr...9..511K
2790:2000GReGr..32..769K
2743:1974PhRvD..10.1066H
2698:1974GReGr...5..491H
2653:1973GReGr...4..333H
2608:2002RPPh...65..599H
2544:2019ApJ...870...78U
2483:2016ApJ...832...96P
2434:2010PhLB..690...73P
2379:2012PhRvD..85j7502P
2332:2010PhLB..694..181P
2160:1986GReGr..18..441P
2088:2007PhT....60c..16H
2041:1971JMP....12.1334H
1990:1976RvMP...48..393H
1939:1961JMP.....2..212K
1896:1964RvMP...36..463S
1850:10.12942/lrr-2004-2
1841:2004LRR.....7....2G
1648:1980PhRvD..21..867N
1603:2019EPJC...79.1023C
1504:observable universe
1502:, before which the
157:Riemannian geometry
93:theoretical physics
4420:Things named after
4282:Subtle is the Lord
4105:(1994 documentary)
4097:(1923 documentary)
4089:(1922 documentary)
3986:Gravitational wave
3869:General relativity
3864:Special relativity
3798:Gravitational wave
3681:Generalisations /
3569:quantum-mechanical
3477:Quantum-mechanical
3290:general relativity
3264:Linearized gravity
2891:10.1007/bf00771019
2843:10.1007/bf00759545
2706:10.1007/bf02451393
2661:10.1007/bf00759853
2168:10.1007/bf00770462
1801:10.24033/asens.761
1760:10.24033/asens.753
1719:10.24033/asens.751
1426:
1380:
1218:
1111:yields the Cartan
1101:
1047:
1010:
976:
939:
854:
759:
726:
694:
662:
621:
597:
574:
485:
407:
382:Lagrangian density
370:
292:Brans–Dicke theory
211:Palatini variation
4488:
4487:
4390:Awards and honors
4373:Siegbert Einstein
4261:Einstein's Cosmos
3811:
3810:
3782:Theory of impetus
3718:
3717:
3690:Liouville gravity
3434:Conformal gravity
3362:Composite gravity
3352:Bimetric theories
3282:
3281:
2731:Physical Review D
2411:Physics Letters B
2356:Physical Review D
2309:Physics Letters B
2270:Physical Review D
2097:10.1063/1.2718743
2049:10.1063/1.1665738
1947:10.1063/1.1703702
1636:Physical Review D
1393:
1392:
1188:
1175:
952:
951:
902:
833:
820:
697:{\displaystyle S}
600:{\displaystyle g}
483:
463:
334:affine connection
188:affine connection
107:, one of several
86:
85:
78:
40:This article may
16:(Redirected from
4513:
4476:
4475:
4375:(distant cousin)
4369:(great-grandson)
4331:Hermann Einstein
4313:Lieserl Einstein
3991:Tea leaf paradox
3838:
3831:
3824:
3815:
3766:
3764:Entropic gravity
3759:
3683:extensions of GR
3671:
3657:
3650:
3643:
3636:
3629:
3622:
3615:
3608:
3594:
3511:
3504:
3497:
3458:Geometrodynamics
3447:
3423:
3404:
3397:
3346:
3339:
3295:
3186:
3168:
3161:
3154:
3145:
3140:
3138:
3125:
3088:
3054:
3027:
3025:
3012:
2986:
2965:
2931:
2910:
2862:
2817:
2783:
2762:
2737:(4): 1066–1069.
2725:
2680:
2635:
2590:
2588:
2566:
2565:
2555:
2537:
2511:
2505:
2504:
2494:
2476:
2452:
2446:
2445:
2427:
2405:
2399:
2398:
2372:
2350:
2344:
2343:
2325:
2303:
2297:
2296:
2286:
2264:
2258:
2257:
2247:
2227:
2221:
2220:
2210:
2194:
2188:
2187:
2143:
2137:
2136:
2108:
2102:
2101:
2099:
2067:
2061:
2060:
2035:(7): 1334–1339.
2024:
2018:
2017:
1973:
1967:
1966:
1922:
1916:
1915:
1879:
1873:
1872:
1862:
1852:
1820:
1814:
1813:
1803:
1779:
1773:
1772:
1762:
1738:
1732:
1731:
1721:
1697:
1691:
1690:
1674:
1668:
1667:
1631:
1625:
1624:
1614:
1596:
1572:
1518:and removes the
1435:
1433:
1432:
1427:
1425:
1424:
1419:
1418:
1417:
1389:
1387:
1386:
1381:
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1371:
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1323:
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1307:
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1301:
1300:
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1210:
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1203:
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1176:
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1167:
1166:
1165:
1147:
1146:
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1126:
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1100:
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1056:
1054:
1053:
1048:
1046:
1045:
1019:
1017:
1016:
1011:
1009:
1008:
985:
983:
982:
977:
975:
974:
948:
946:
945:
940:
938:
937:
919:
918:
903:
895:
890:
889:
869:
863:
861:
860:
855:
847:
846:
834:
826:
821:
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792:
791:
780:
768:
766:
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758:
757:
735:
733:
732:
727:
703:
701:
700:
695:
671:
669:
668:
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660:
651:
630:
628:
627:
622:
606:
604:
603:
598:
583:
581:
580:
575:
567:
566:
556:
552:
551:
550:
549:
543:
542:
532:
531:
530:
524:
523:
494:
492:
491:
486:
484:
482:
474:
469:
464:
462:
451:
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445:
444:
438:
437:
416:
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413:
408:
406:
405:
404:
398:
397:
379:
377:
376:
371:
369:
368:
367:
361:
360:
173:Lorentz symmetry
81:
74:
70:
67:
61:
57:balanced fashion
35:
34:
27:
21:
4521:
4520:
4516:
4515:
4514:
4512:
4511:
4510:
4506:Albert Einstein
4491:
4490:
4489:
4484:
4464:
4415:Religious views
4410:Political views
4378:
4363:(granddaughter)
4361:Evelyn Einstein
4349:Robert Einstein
4343:Eduard Einstein
4287:
4224:
4218:
4172:
4142:Einstein's Gift
4076:
4069:
4010:Annus mirabilis
3995:
3966:Teleparallelism
3911:Einstein radius
3881:Brownian motion
3847:
3845:Albert Einstein
3842:
3812:
3807:
3786:
3762:
3755:
3726:
3724:
3714:
3695:Lovelock theory
3682:
3676:
3667:
3653:
3646:
3639:
3632:
3625:
3618:
3611:
3604:
3590:
3568:
3562:
3541:
3507:
3500:
3493:
3472:
3463:Induced gravity
3443:
3439:Scalar theories
3419:
3400:
3393:
3384:Massive gravity
3344:Teleparallelism
3342:
3337:Einstein–Cartan
3335:
3319:
3310:Quantum gravity
3289:
3288:Alternatives to
3278:
3244:Exact solutions
3215:
3177:
3172:
3128:
3091:
3039:Physics Reports
3036:
3015:
2968:
2913:
2877:(11): 869–883.
2868:
2820:
2765:
2728:
2683:
2638:
2593:
2578:
2575:
2573:Further reading
2570:
2569:
2513:
2512:
2508:
2454:
2453:
2449:
2407:
2406:
2402:
2352:
2351:
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2300:
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2229:
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2224:
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2191:
2145:
2144:
2140:
2110:
2109:
2105:
2069:
2068:
2064:
2026:
2025:
2021:
1975:
1974:
1970:
1924:
1923:
1919:
1881:
1880:
1876:
1822:
1821:
1817:
1781:
1780:
1776:
1740:
1739:
1735:
1699:
1698:
1694:
1676:
1675:
1671:
1633:
1632:
1628:
1574:
1573:
1569:
1564:
1537:
1473:static universe
1457:
1406:
1404:
1399:
1398:
1360:
1358:
1332:
1330:
1313:
1311:
1288:
1286:
1269:
1267:
1244:
1242:
1237:
1236:
1192:
1190:
1154:
1152:
1148:
1131:
1127:
1120:
1119:
1113:spin connection
1081:
1079:
1074:
1073:
1034:
1029:
1028:
997:
992:
991:
963:
958:
957:
926:
907:
878:
873:
872:
835:
806:
802:
785:
781:
774:
773:
746:
741:
740:
709:
708:
686:
685:
652:
633:
632:
613:
612:
589:
588:
558:
536:
517:
516:
512:
498:
497:
455:
431:
426:
425:
391:
386:
385:
354:
349:
348:
321:
319:Field equations
305:Steven Weinberg
297:quantum gravity
275:teleparallelism
267:Albert Einstein
259:
207:Palatini action
144:Einstein–Cartan
121:
89:
82:
71:
65:
62:
52:help improve it
49:
36:
32:
23:
22:
15:
12:
11:
5:
4519:
4517:
4509:
4508:
4503:
4493:
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4485:
4483:
4482:
4469:
4466:
4465:
4463:
4462:
4457:
4452:
4447:
4442:
4437:
4432:
4427:
4422:
4417:
4412:
4407:
4402:
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4392:
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4384:
4380:
4379:
4377:
4376:
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4364:
4358:
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4328:
4322:
4316:
4310:
4304:
4297:
4295:
4289:
4288:
4286:
4285:
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4271:
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4250:
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4228:
4226:
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4219:
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4216:
4211:
4206:
4201:
4196:
4191:
4186:
4180:
4178:
4174:
4173:
4171:
4170:
4162:
4154:
4153:(2008 TV film)
4146:
4138:
4130:
4122:
4118:Young Einstein
4114:
4110:Insignificance
4106:
4098:
4090:
4081:
4079:
4071:
4070:
4068:
4067:
4061:
4058:Why Socialism?
4054:
4046:
4038:
4030:
4022:
4015:
4005:
4003:
3997:
3996:
3994:
3993:
3988:
3983:
3978:
3973:
3968:
3963:
3958:
3953:
3948:
3943:
3938:
3933:
3928:
3923:
3918:
3913:
3908:
3903:
3898:
3896:Einstein solid
3893:
3888:
3883:
3878:
3873:
3872:
3871:
3866:
3855:
3853:
3849:
3848:
3843:
3841:
3840:
3833:
3826:
3818:
3809:
3808:
3806:
3805:
3800:
3794:
3792:
3791:Related topics
3788:
3787:
3785:
3784:
3779:
3774:
3769:
3768:
3767:
3760:
3748:
3743:
3738:
3732:
3730:
3720:
3719:
3716:
3715:
3713:
3712:
3707:
3702:
3697:
3692:
3686:
3684:
3678:
3677:
3675:
3674:
3673:
3672:
3663:Twistor theory
3660:
3659:
3658:
3651:
3644:
3637:
3630:
3623:
3616:
3609:
3597:
3596:
3595:
3583:
3578:
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3539:
3534:
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3321:
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3307:
3301:
3299:
3292:
3284:
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3277:
3276:
3271:
3266:
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3256:
3251:
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3241:
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3231:
3225:
3223:
3217:
3216:
3214:
3213:
3208:
3203:
3198:
3192:
3190:
3183:
3179:
3178:
3173:
3171:
3170:
3163:
3156:
3148:
3142:
3141:
3126:
3089:
3052:hep-th/0103093
3045:(2): 113–213.
3034:
3031:
3028:
3013:
2966:
2922:(3): 737–751.
2911:
2866:
2863:
2829:(6): 511–517.
2818:
2774:(5): 769–839.
2763:
2726:
2692:(5): 491–516.
2681:
2647:(4): 333–349.
2636:
2602:(5): 599–649.
2591:
2574:
2571:
2568:
2567:
2506:
2447:
2400:
2363:(10): 107502.
2345:
2316:(3): 181–185.
2298:
2259:
2222:
2189:
2154:(5): 441–460.
2138:
2103:
2062:
2019:
1984:(3): 393–416.
1968:
1933:(2): 212–221.
1917:
1890:(1): 463–469.
1874:
1815:
1774:
1733:
1692:
1669:
1642:(4): 867–873.
1626:
1566:
1565:
1563:
1560:
1559:
1558:
1553:
1548:
1543:
1536:
1533:
1456:
1453:
1443:rather than a
1423:
1416:
1413:
1409:
1395:
1394:
1391:
1390:
1377:
1370:
1367:
1363:
1357:
1354:
1349:
1342:
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1327:
1320:
1316:
1310:
1305:
1298:
1295:
1291:
1283:
1276:
1272:
1266:
1261:
1254:
1251:
1247:
1229:
1228:
1217:
1214:
1209:
1202:
1199:
1195:
1187:
1184:
1179:
1171:
1164:
1161:
1157:
1151:
1143:
1136:
1130:
1098:
1091:
1088:
1084:
1044:
1041:
1037:
1007:
1004:
1000:
973:
970:
966:
954:
953:
950:
949:
936:
933:
929:
925:
922:
917:
914:
910:
906:
901:
898:
893:
888:
885:
881:
865:
864:
853:
850:
845:
842:
838:
832:
829:
824:
816:
813:
809:
805:
797:
790:
784:
756:
753:
749:
737:
736:
725:
722:
719:
716:
693:
678:speed of light
672:involving the
659:
655:
650:
646:
643:
640:
620:
596:
585:
584:
573:
570:
565:
561:
555:
548:
541:
535:
529:
522:
515:
511:
508:
505:
495:
481:
477:
473:
467:
461:
458:
454:
449:
443:
436:
403:
396:
384:of matter and
380:represent the
366:
359:
320:
317:
313:twistor theory
301:Dirac equation
258:
255:
235:
234:
226:
225:
218:torsion tensor
181:spin structure
169:gauge symmetry
149:
148:
147:
146:
134:
133:
129:
128:
120:
117:
87:
84:
83:
39:
37:
30:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4518:
4507:
4504:
4502:
4499:
4498:
4496:
4481:
4480:
4471:
4470:
4467:
4461:
4458:
4456:
4453:
4451:
4448:
4446:
4443:
4441:
4438:
4436:
4433:
4431:
4428:
4426:
4423:
4421:
4418:
4416:
4413:
4411:
4408:
4406:
4403:
4401:
4398:
4396:
4393:
4391:
4388:
4387:
4385:
4381:
4374:
4371:
4368:
4365:
4362:
4359:
4356:
4353:
4350:
4347:
4344:
4341:
4338:
4337:Maja Einstein
4335:
4332:
4329:
4326:
4323:
4320:
4317:
4314:
4311:
4308:
4307:Elsa Einstein
4305:
4302:
4299:
4298:
4296:
4294:
4290:
4284:
4283:
4279:
4277:
4276:
4272:
4270:
4269:
4265:
4263:
4262:
4258:
4256:
4255:
4251:
4249:
4248:
4244:
4242:
4241:
4237:
4235:
4234:
4230:
4229:
4227:
4221:
4215:
4212:
4210:
4207:
4205:
4202:
4200:
4197:
4195:
4194:Kalinga Prize
4192:
4190:
4187:
4185:
4182:
4181:
4179:
4175:
4168:
4167:
4163:
4161:(2017 series)
4160:
4159:
4155:
4152:
4151:
4147:
4144:
4143:
4139:
4136:
4135:
4131:
4128:
4127:
4123:
4120:
4119:
4115:
4112:
4111:
4107:
4104:
4103:
4099:
4096:
4095:
4091:
4088:
4087:
4083:
4082:
4080:
4078:
4072:
4065:
4062:
4059:
4055:
4052:
4051:
4047:
4044:
4043:
4039:
4036:
4035:
4031:
4028:
4027:
4023:
4020:
4016:
4013:
4011:
4007:
4006:
4004:
4002:
3998:
3992:
3989:
3987:
3984:
3982:
3979:
3977:
3974:
3972:
3969:
3967:
3964:
3962:
3959:
3957:
3954:
3952:
3949:
3947:
3944:
3942:
3939:
3937:
3934:
3932:
3929:
3927:
3924:
3922:
3919:
3917:
3914:
3912:
3909:
3907:
3904:
3902:
3899:
3897:
3894:
3892:
3889:
3887:
3884:
3882:
3879:
3877:
3874:
3870:
3867:
3865:
3862:
3861:
3860:
3857:
3856:
3854:
3850:
3846:
3839:
3834:
3832:
3827:
3825:
3820:
3819:
3816:
3804:
3801:
3799:
3796:
3795:
3793:
3789:
3783:
3780:
3778:
3775:
3773:
3770:
3765:
3761:
3758:
3757:Fatio–Le Sage
3754:
3753:
3752:
3749:
3747:
3744:
3742:
3739:
3737:
3734:
3733:
3731:
3729:
3723:Pre-Newtonian
3721:
3711:
3708:
3706:
3703:
3701:
3698:
3696:
3693:
3691:
3688:
3687:
3685:
3679:
3670:
3666:
3665:
3664:
3661:
3656:
3652:
3649:
3645:
3642:
3638:
3635:
3631:
3628:
3624:
3621:
3617:
3614:
3610:
3607:
3603:
3602:
3601:
3600:String theory
3598:
3593:
3589:
3588:
3587:
3584:
3582:
3579:
3577:
3574:
3573:
3571:
3565:
3559:
3556:
3554:
3551:
3550:
3548:
3544:
3538:
3535:
3533:
3530:
3528:
3525:
3523:
3520:
3518:
3515:
3510:
3506:
3503:
3499:
3496:
3492:
3491:
3490:
3487:
3485:
3482:
3481:
3479:
3475:
3469:
3466:
3464:
3461:
3459:
3456:
3454:
3451:
3446:
3442:
3441:
3440:
3437:
3435:
3432:
3430:
3427:
3422:
3418:
3417:
3416:
3413:
3411:
3408:
3403:
3399:
3396:
3392:
3391:
3390:
3387:
3385:
3382:
3380:
3377:
3375:
3373:
3369:
3365:
3363:
3360:
3358:
3355:
3353:
3350:
3345:
3341:
3338:
3334:
3333:
3332:
3329:
3328:
3326:
3322:
3316:
3313:
3311:
3308:
3306:
3303:
3302:
3300:
3296:
3293:
3291:
3285:
3275:
3272:
3270:
3269:ADM formalism
3267:
3265:
3262:
3260:
3257:
3255:
3252:
3250:
3247:
3245:
3242:
3240:
3237:
3235:
3232:
3230:
3227:
3226:
3224:
3222:
3218:
3212:
3209:
3207:
3204:
3202:
3199:
3197:
3194:
3193:
3191:
3187:
3184:
3180:
3176:
3169:
3164:
3162:
3157:
3155:
3150:
3149:
3146:
3137:
3136:gr-qc/0606062
3132:
3127:
3123:
3119:
3115:
3111:
3107:
3103:
3099:
3095:
3090:
3086:
3082:
3078:
3074:
3070:
3066:
3062:
3058:
3053:
3048:
3044:
3040:
3035:
3032:
3029:
3024:
3019:
3014:
3010:
3006:
3002:
2998:
2994:
2990:
2985:
2980:
2976:
2972:
2967:
2963:
2959:
2955:
2951:
2947:
2943:
2939:
2935:
2930:
2925:
2921:
2917:
2912:
2908:
2904:
2900:
2896:
2892:
2888:
2884:
2880:
2876:
2872:
2867:
2864:
2860:
2856:
2852:
2848:
2844:
2840:
2836:
2832:
2828:
2824:
2819:
2815:
2811:
2807:
2803:
2799:
2795:
2791:
2787:
2782:
2781:gr-qc/9801003
2777:
2773:
2769:
2764:
2760:
2756:
2752:
2748:
2744:
2740:
2736:
2732:
2727:
2723:
2719:
2715:
2711:
2707:
2703:
2699:
2695:
2691:
2687:
2682:
2678:
2674:
2670:
2666:
2662:
2658:
2654:
2650:
2646:
2642:
2637:
2633:
2629:
2625:
2621:
2617:
2613:
2609:
2605:
2601:
2597:
2592:
2587:
2586:gr-qc/9602013
2582:
2577:
2576:
2572:
2563:
2559:
2554:
2549:
2545:
2541:
2536:
2531:
2527:
2523:
2522:
2517:
2510:
2507:
2502:
2498:
2493:
2488:
2484:
2480:
2475:
2470:
2466:
2462:
2458:
2451:
2448:
2443:
2439:
2435:
2431:
2426:
2421:
2417:
2413:
2412:
2404:
2401:
2396:
2392:
2388:
2384:
2380:
2376:
2371:
2366:
2362:
2358:
2357:
2349:
2346:
2341:
2337:
2333:
2329:
2324:
2319:
2315:
2311:
2310:
2302:
2299:
2294:
2290:
2285:
2280:
2277:(8): 083509.
2276:
2272:
2271:
2263:
2260:
2255:
2251:
2246:
2241:
2237:
2233:
2226:
2223:
2218:
2214:
2209:
2204:
2200:
2193:
2190:
2185:
2181:
2177:
2173:
2169:
2165:
2161:
2157:
2153:
2149:
2142:
2139:
2134:
2130:
2126:
2122:
2118:
2114:
2107:
2104:
2098:
2093:
2089:
2085:
2081:
2077:
2076:Physics Today
2073:
2066:
2063:
2058:
2054:
2050:
2046:
2042:
2038:
2034:
2030:
2023:
2020:
2015:
2011:
2007:
2003:
1999:
1995:
1991:
1987:
1983:
1979:
1972:
1969:
1964:
1960:
1956:
1952:
1948:
1944:
1940:
1936:
1932:
1928:
1921:
1918:
1913:
1909:
1905:
1901:
1897:
1893:
1889:
1885:
1878:
1875:
1870:
1866:
1861:
1856:
1851:
1846:
1842:
1838:
1834:
1830:
1826:
1819:
1816:
1811:
1807:
1802:
1797:
1793:
1790:(in French).
1789:
1785:
1778:
1775:
1770:
1766:
1761:
1756:
1752:
1749:(in French).
1748:
1744:
1737:
1734:
1729:
1725:
1720:
1715:
1711:
1708:(in French).
1707:
1703:
1696:
1693:
1688:
1685:(in French).
1684:
1680:
1673:
1670:
1665:
1661:
1657:
1653:
1649:
1645:
1641:
1637:
1630:
1627:
1622:
1618:
1613:
1608:
1604:
1600:
1595:
1590:
1586:
1582:
1578:
1571:
1568:
1561:
1557:
1554:
1552:
1549:
1547:
1544:
1542:
1539:
1538:
1534:
1532:
1530:
1529:event horizon
1526:
1521:
1517:
1513:
1509:
1505:
1501:
1497:
1493:
1489:
1485:
1480:
1478:
1474:
1470:
1466:
1462:
1454:
1452:
1450:
1446:
1442:
1439:
1421:
1414:
1411:
1407:
1375:
1368:
1365:
1361:
1355:
1352:
1347:
1340:
1337:
1333:
1325:
1318:
1314:
1308:
1303:
1296:
1293:
1289:
1281:
1274:
1270:
1264:
1259:
1252:
1249:
1245:
1235:
1234:
1231:
1230:
1215:
1212:
1207:
1200:
1197:
1193:
1185:
1182:
1177:
1169:
1162:
1159:
1155:
1149:
1128:
1118:
1117:
1116:
1114:
1096:
1089:
1086:
1082:
1070:
1068:
1064:
1060:
1042:
1039:
1035:
1026:
1024:
1005:
1002:
998:
989:
971:
968:
964:
934:
931:
927:
923:
920:
915:
912:
908:
904:
899:
896:
891:
886:
883:
879:
871:
870:
867:
866:
851:
848:
843:
840:
836:
830:
827:
822:
814:
811:
807:
803:
782:
772:
771:
770:
754:
751:
747:
723:
720:
717:
714:
707:
706:
705:
691:
683:
679:
675:
657:
653:
648:
644:
641:
638:
618:
610:
594:
571:
568:
563:
559:
553:
533:
513:
509:
506:
503:
496:
475:
465:
459:
456:
452:
447:
424:
423:
422:
420:
383:
345:
343:
339:
335:
330:
326:
318:
316:
314:
310:
306:
302:
298:
293:
288:
286:
282:
281:Dennis Sciama
278:
276:
272:
268:
264:
256:
254:
250:
246:
244:
240:
232:
228:
227:
223:
222:
221:
219:
214:
212:
208:
203:
201:
197:
193:
189:
184:
182:
178:
174:
170:
166:
162:
158:
153:
145:
141:
140:
139:
138:
137:
131:
130:
126:
125:
124:
118:
116:
114:
110:
106:
102:
98:
94:
80:
77:
69:
59:
58:
53:
47:
45:
38:
29:
28:
19:
4477:
4445:Einsteinhaus
4325:Pauline Koch
4303:(first wife)
4301:Mileva Marić
4280:
4273:
4266:
4259:
4252:
4245:
4238:
4231:
4164:
4156:
4148:
4140:
4132:
4124:
4116:
4108:
4100:
4092:
4084:
4048:
4040:
4032:
4024:
4009:
3940:
3725:theories and
3558:Supergravity
3371:
3367:
3336:
3229:Introduction
3100:(114): 7–8.
3097:
3093:
3042:
3038:
2974:
2970:
2919:
2915:
2874:
2870:
2826:
2822:
2771:
2767:
2734:
2730:
2689:
2685:
2644:
2640:
2599:
2595:
2525:
2519:
2509:
2464:
2460:
2450:
2418:(1): 73–77.
2415:
2409:
2403:
2360:
2354:
2348:
2313:
2307:
2301:
2274:
2268:
2262:
2235:
2231:
2225:
2198:
2192:
2151:
2147:
2141:
2116:
2112:
2106:
2079:
2075:
2065:
2032:
2028:
2022:
1981:
1977:
1971:
1930:
1926:
1920:
1887:
1883:
1877:
1832:
1828:
1818:
1791:
1787:
1777:
1750:
1746:
1736:
1709:
1705:
1695:
1686:
1682:
1672:
1639:
1635:
1629:
1587:(12): 1023.
1584:
1580:
1570:
1500:scale factor
1481:
1477:cyclic model
1461:cosmological
1458:
1396:
1071:
1062:
1022:
988:Ricci tensor
955:
738:
586:
419:Ricci scalar
346:
322:
289:
279:
260:
251:
247:
236:
215:
204:
185:
154:
150:
143:
135:
122:
100:
96:
90:
72:
63:
55:
44:undue weight
41:
4450:Einsteinium
4223:Books about
4169:(2023 film)
4166:Oppenheimer
4145:(2003 play)
4137:(1994 film)
4129:(1993 play)
4121:(1988 film)
4113:(1985 film)
3956:EPR paradox
3527:Causal sets
3421:Brans–Dicke
3239:Mathematics
1712:: 325–412.
1516:black holes
1512:"pointlike"
1059:spin tensor
609:determinant
263:Élie Cartan
243:spin tensor
113:Élie Cartan
4495:Categories
4455:Max Talmey
4357:(grandson)
4315:(daughter)
4075:In popular
3741:CGHS model
3728:toy models
2929:1804.06730
2535:1808.08327
2284:2003.07463
2238:(6): 020.
2208:2307.12190
1689:: 593–595.
1594:1902.02222
1562:References
1496:Big Bounce
1441:constraint
1115:equations
285:Tom Kibble
209:(see also
196:contorsion
66:April 2024
3746:RST model
3532:DGP model
3509:Spin foam
3453:Whitehead
3445:Nordström
3374:) gravity
3324:Classical
3298:Paradigms
3249:Resources
3122:0300-8746
3085:119356912
3077:0370-1573
3023:0911.0334
3009:119218875
2984:1301.1588
2962:118897253
2954:0264-9381
2907:189851295
2899:0001-7701
2859:118380177
2851:0001-7701
2806:0001-7701
2759:0556-2821
2722:120844152
2714:0001-7701
2677:120910420
2669:0001-7701
2632:250831296
2624:0034-4885
2562:119514549
2528:(2): 78.
2501:119771613
2474:1410.3881
2467:(2): 96.
2425:0910.1181
2395:118434253
2370:1111.4595
2323:1007.0587
2245:1401.7639
2184:120013580
2176:0001-7701
2082:(3): 16.
2057:0022-2488
2006:0034-6861
1955:0022-2488
1912:0034-6861
1810:0012-9593
1794:: 17–88.
1769:0012-9593
1728:0012-9593
1664:0556-2821
1621:1434-6044
1508:inflation
1492:fermionic
1438:algebraic
1408:σ
1362:σ
1356:κ
1309:−
1194:σ
1178:−
1150:δ
1129:δ
1063:symmetric
1023:canonical
924:κ
892:−
823:−
804:δ
783:δ
715:δ
642:π
619:κ
510:∫
460:κ
342:curvature
115:in 1922.
4479:Category
4405:Memorial
4351:(cousin)
4339:(sister)
4333:(father)
4327:(mother)
4225:Einstein
4060:" (1949)
4021:" (1905)
3803:Graviton
3613:F-theory
3606:M-theory
3182:Standard
2814:14846186
2133:73035217
2014:55726649
1963:54806287
1869:28179864
1835:(1): 2.
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