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Open AccessArticle

The Geometrical Trinity of Gravity

1
Departamento de Física Fundamental and IUFFyM, Universidad de Salamanca, E-37008 Salamanca, Spain
2
Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland
3
Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden
4
Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
*
Authors to whom correspondence should be addressed.
Universe 2019, 5(7), 173; https://doi.org/10.3390/universe5070173
Received: 5 June 2019 / Revised: 2 July 2019 / Accepted: 5 July 2019 / Published: 15 July 2019
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. Based on these three alternative formulations of General Relativity, we then discuss some extensions. View Full-Text
Keywords: general relativity; modified gravity; torsion; non-metricity general relativity; modified gravity; torsion; non-metricity
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Beltrán Jiménez, J.; Heisenberg, L.; Koivisto, T.S. The Geometrical Trinity of Gravity. Universe 2019, 5, 173.

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