https://doi.org/10.1140/epjp/s13360-024-05467-7
Regular Article
Unified first law of thermodynamics in Gauss–Bonnet gravity on an FLRW background
Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla, 4950, Valparaíso, Chile
Received:
12
April
2024
Accepted:
16
July
2024
Published online:
26
July
2024
Employing the thermodynamics unified first law through the thermodynamics-gravity conjecture, in this article, we derive for an FLRW universe the Friedmann equations in the framework of Gauss–Bonnet gravity theory. To do this, we project this generalized first law along the Kodama vector field and the direction of an orthogonal vector to the Kodama vector. The second Friedmann equation is obtained by projecting on the Kodama vector, while the first is obtained by projecting along the flux on the Cauchy hypersurfaces. This result does not assume a priory temperature and an entropy, so the Clausius relation is not used here. Nevertheless, it is used to obtain the corresponding Gauss–Bonnet entropy.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
