Thermodynamic formulation of Cotton gravity in the Codazzi parametrization
Abstract
We develop a thermodynamic formulation of Cotton gravity in the Codazzi parametrization, providing a general framework in which the gravitational dynamics can be interpreted in terms of horizon thermodynamics. As paradigmatic examples, we apply the formalism to FriedmannRobertson-Walker (FRW) and static spherically symmetric spacetimes. By implementing the first law of thermodynamics on the apparent cosmological and event horizons, we derive a modified holographic entropy consisting of the standard Bekenstein-Hawking term supplemented by a correction induced by the Codazzi tensor. In the cosmological setting, this correction is governed by the temporal component of the Codazzi tensor, while in static configurations it is controlled by its anisotropic sector. Remarkably, the sign of this contribution provides a potential diagnostic of the underlying matter content, allowing one to distinguish between ordinary matter, a cosmological constant and phantom-like components. These results establish horizon thermodynamics as a sensitive probe of Cotton gravity, offering a complementary perspective beyond background kinematics and enabling a characterization of the statistical and thermodynamic properties of spacetime within the Codazzi formulation.
Versions
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BibTeX
@misc{ghaffari2026thermodynamic,
title = {{Thermodynamic formulation of Cotton gravity in the Codazzi parametrization}},
author = {Shayesteh Ghaffari and Giuseppe Gaetano Luciano and Carlo Alberto Mantica},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2605.11821},
eprint = {2605.11821},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.11821},
}
RIS
TY - UNPB
TI - Thermodynamic formulation of Cotton gravity in the Codazzi parametrization
AU - Shayesteh Ghaffari
AU - Giuseppe Gaetano Luciano
AU - Carlo Alberto Mantica
PY - 2026
DA - 2026/07/08
PB - arXiv
DO - 10.48550/arxiv.2605.11821
UR - https://arxiv.org/abs/2605.11821
AB - We develop a thermodynamic formulation of Cotton gravity in the Codazzi parametrization, providing a general framework in which the gravitational dynamics can be interpreted in terms of horizon thermodynamics. As paradigmatic examples, we apply the formalism to FriedmannRobertson-Walker (FRW) and static spherically symmetric spacetimes. By implementing the first law of thermodynamics on the apparent cosmological and event horizons, we derive a modified holographic entropy consisting of the standard Bekenstein-Hawking term supplemented by a correction induced by the Codazzi tensor. In the cosmological setting, this correction is governed by the temporal component of the Codazzi tensor, while in static configurations it is controlled by its anisotropic sector. Remarkably, the sign of this contribution provides a potential diagnostic of the underlying matter content, allowing one to distinguish between ordinary matter, a cosmological constant and phantom-like components. These results establish horizon thermodynamics as a sensitive probe of Cotton gravity, offering a complementary perspective beyond background kinematics and enabling a characterization of the statistical and thermodynamic properties of spacetime within the Codazzi formulation.
ER -