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Wald's entropy in Coincident General Relativity | | Lavinia Heisenberg
; Simon Kuhn
; Laurens Walleghem
; | | Date: |
25 Mar 2022 | | Abstract: | The equivalence principle and its universality enables the geometrical
formulation of gravity. In the standard formulation of General Relativity ’a
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 General Relativity
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 General
Relativity oblivious to the affine spacetime structure, the Coincident General
Relativity. 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 General Relativity. 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 Coincident General Relativity
with an improved action principle gives the same entropy as the well-known
entropy in standard General Relativity. Furthermore the first law of black hole
thermodynamics holds and an explicit expression for the energy appearing in the
first law is obtained. | | Source: | arXiv, 2203.13914 | | Services: | Forum | Review | PDF | Favorites | |
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