Wald’s entropy in coincident general relativity

• Verfasst von: Heisenberg, Lavinia [VerfasserIn]
• Verfasst von: Kuhn, Simon [VerfasserIn]
• Verfasst von: Walleghem, Laurens [VerfasserIn]
• Titel: Wald’s entropy in coincident general relativity
• Verf.angabe: Lavinia Heisenberg, Simon Kuhn and Laurens Walleghem
• E-Jahr: 2022
• Jahr: 3 November 2022
• Umfang: 37 S.
• Fussnoten: Gesehen am 15.02.2023
• Titel Quelle: Enthalten in: Classical and quantum gravity
• Ort Quelle: Bristol : IOP Publ., 1984
• Jahr Quelle: 2022
• Band/Heft Quelle: 39(2022), 23, Artikel-ID 235002, Seite 1-37
• ISSN Quelle: 1361-6382
• DOI: doi:10.1088/1361-6382/ac987d
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1835726151

Abstract

The equivalence principle and its universality enables the geometrical formulation of gravity. In the standard formulation of General Relativity (GR) á la Einstein, the gravitational interaction is geometrized in terms of the spacetime curvature. However, if we embrace the geometrical character of gravity, two alternative, though equivalent, formulations of GR emerge in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity. The latter allows a much simpler formulation of GR oblivious to the affine spacetime structure, the Coincident General Relativity (CGR). The entropy of a black hole can be computed using the Euclidean path integral approach, which strongly relies on the addition of boundary or regulating terms in the standard formulation of GR. A more fundamental derivation can be performed using Wald’s formula, in which the entropy is directly related to Noether charges and is applicable to general theories with diffeomorphism invariance. In this work we extend Wald’s Noether charge method for calculating black hole entropy to spacetimes endowed with non-metricity. Using this method, we show that CGR with an improved action principle gives the same entropy as the well-known entropy in standard GR. Furthermore the first law of black hole thermodynamics holds and an explicit expression for the energy appearing in the first law is obtained.