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2019

The Geometrical Trinity of Gravity

Jimenez, Jose Beltran, Heisenberg, Lavinia, Koivisto, Tomi S.

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The geometrical nature of gravity emerges from the universality dictated by the equivalence principle.

In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the spacetime curvature, which is now the standard interpretation of gravity.
However, this is not the only possibility.
In these notes we discuss two alternative, though equivalent, formulations of General Relativity in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity, thus putting forward the existence of three seemingly unrelated representations of the same underlying theory.

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It is noteworthy that Einstein considered these five non-metricity terms with a trivial connection, which corresponds to our coincident gauge: A. Einstein, Plenary Session of Nov. 19, 1914-Comm. of the phys. math sec of Oct. 29, ”The Formal Foundation of the General Theory of Relativity”
1914
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Action Integrals and Partition Functions in Quantum Gravity,” Phys. Rev. D 15
1977
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J. M. Nester and H. J. Yo, “Symmetric teleparallel general relativity,” Chin. J. Phys. 37
1999
Earlier work this paper cites.
Y. N. Obukhov and J. G. Pereira, “Lessons of spin and torsion: Reply to ‘Consistent coupling to Dirac fields in teleparallelism’,” Phys. Rev. D 69
2004
Earlier work this paper cites.

Similar

E. Schrödinger, Space-time Structure Cambridge University Press, 1950; G. J. Olmo, “Palatini Approach to Modified Gravity: f(R) Theories and Beyond,” Int. J. Mod. Phys. D 20
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2011
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R. Aldrovandi and J. G. Pereira, “Teleparallel Gravity : An Introduction,” Fundam. Theor. Phys. 173
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D. Lehmkuhl, “Why Einstein did not believe that general relativity geometrizes gravity,” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 69
2014
Cited alongside, same era.
A. Golovnev, T. Koivisto and M. Sandstad, “On the covariance of teleparallel gravity theories,” Class. Quant. Grav. 34
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2017
Cited alongside, same era.
M. Krssak, R. J. Van Den Hoogen, J. G. Pereira, C. G. Boehmer and A. A. Coley, “Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach,” arXiv:1810.12932 [gr-qc]
Original
Cited in the paper.
T. Ortin, “Gravity and Strings,” doi:10.1017/CBO9781139019750
Cited in the paper.
T. Koivisto and G. Tsimperis, “The spectrum of teleparallel gravity,” arXiv:1810.11847 [gr-qc]
Original
Cited in the paper.

Then

J. Beltran Jimenez, L. Heisenberg, G. J. Olmo and D. Rubiera-Garcia, “Born-Infeld inspired modifications of gravity,” Phys. Rept. 727
Original
2018
Later among the works it cites.
J. Beltran Jimenez, L. Heisenberg and T. Koivisto, “Teleparallel Palatini theories,” JCAP 1808
Original
2018
Later among the works it cites.
J. Beltran Jimenez, L. Heisenberg and T. Koivisto, “Coincident General Relativity,” Phys. Rev. D 98
Original
2018
Later among the works it cites.

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