A comparison of two constructions for dynamical corrections to Wald entropy
Abstract
In this work, we analyze the differences and similarities between two recent constructions, which are distinct in their methodologies for extending the Wald entropy of stationary black holes to non-stationary situations in general higher-derivative gravity. One of them, denoted by SWall, is constructed by exploiting the boost symmetry of the near-horizon geometry, whereas the other, denoted by Sdyn, is obtained from a covariant phase-space analysis based on the Wald-Iyer Noether charge formalism. While Sdyn is, by construction, defined only for linearized fluctuations around a stationary black hole solution, SWall does not require such a linearization for its construction. Although the linearization is necessary to interpret SWall as a well-defined notion of entropy, the construction itself naturally contains terms that are higher order in the dynamical fluctuations. By comparing the technical structures underlying the two constructions, we clarify the fundamental differences between the methods on which they are based. We demonstrate that while the construction of Sdyn given the SWall is straightforward, the converse is more subtle. We develop an algorithm to obtain a local expression for SWall from a known expression for Sdyn in a generic diffeomorphism-invariant theory of gravity, provided certain technical conditions are satisfied. We justify our analytical findings with explicit demonstrations in a particular case: the Riemann-squared example of the higher-derivative theory of gravity.
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BibTeX
@misc{bhattacharyya2026comparison,
title = {{A comparison of two constructions for dynamical corrections to Wald entropy}},
author = {Sayantani Bhattacharyya and Parthajit Biswas and Nilay Kundu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.27732},
eprint = {2607.27732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.27732},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A comparison of two constructions for dynamical corrections to Wald entropy
AU - Sayantani Bhattacharyya
AU - Parthajit Biswas
AU - Nilay Kundu
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2607.27732
UR - https://arxiv.org/abs/2607.27732
AB - In this work, we analyze the differences and similarities between two recent constructions, which are distinct in their methodologies for extending the Wald entropy of stationary black holes to non-stationary situations in general higher-derivative gravity. One of them, denoted by S_Wall, is constructed by exploiting the boost symmetry of the near-horizon geometry, whereas the other, denoted by S_dyn, is obtained from a covariant phase-space analysis based on the Wald-Iyer Noether charge formalism. While S_dyn is, by construction, defined only for linearized fluctuations around a stationary black hole solution, S_Wall does not require such a linearization for its construction. Although the linearization is necessary to interpret S_Wall as a well-defined notion of entropy, the construction itself naturally contains terms that are higher order in the dynamical fluctuations. By comparing the technical structures underlying the two constructions, we clarify the fundamental differences between the methods on which they are based. We demonstrate that while the construction of S_dyn given the S_Wall is straightforward, the converse is more subtle. We develop an algorithm to obtain a local expression for S_Wall from a known expression for S_dyn in a generic diffeomorphism-invariant theory of gravity, provided certain technical conditions are satisfied. We justify our analytical findings with explicit demonstrations in a particular case: the Riemann-squared example of the higher-derivative theory of gravity.
ER -