The entropy of dynamical black holes deviating from electrovacuum in second order
Abstract
We study the entropy of dynamical black holes in Einstein--Maxwell theory. Starting from a stationary electrovacuum background with a bifurcate Killing horizon, the apparent horizon is constructed perturbatively in Gaussian null coordinates, and the area of its cross section is derived to second order. Within the covariant phase space formalism, we introduce a modified canonical energy that incorporates contributions from external matter and is naturally related to the second-order variation of the entropy through the balance law. Under the null energy condition and the asymptotic stationary condition, the entropy is proportional to the area of the apparent horizon up to second-order and satisfies the second law. Without the null energy condition, establishing this area law requires additional assumptions.
Related
- Electrovacuum Black Hole Uniqueness
- The entropy of black hole under second-order deviation from equilibrium
- Finite-size scaling theory of Rényi thermal entropy for second-order, first-order, and weakly first-order quantum phase transitions
- Second largest eigenvalue does not bound stationary entropy production
- Lower bounds on entropy production from dynamical correlation functions
BibTeX
@misc{fu2026entropy,
title = {{The entropy of dynamical black holes deviating from electrovacuum in second order}},
author = {Wen-Tao Fu and Ming-Fei Ji and Yu-Sen Zhou and Li-Ming Cao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.12794},
eprint = {2607.12794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.12794},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The entropy of dynamical black holes deviating from electrovacuum in second order
AU - Wen-Tao Fu
AU - Ming-Fei Ji
AU - Yu-Sen Zhou
AU - Li-Ming Cao
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2607.12794
UR - https://arxiv.org/abs/2607.12794
AB - We study the entropy of dynamical black holes in Einstein--Maxwell theory. Starting from a stationary electrovacuum background with a bifurcate Killing horizon, the apparent horizon is constructed perturbatively in Gaussian null coordinates, and the area of its cross section is derived to second order. Within the covariant phase space formalism, we introduce a modified canonical energy that incorporates contributions from external matter and is naturally related to the second-order variation of the entropy through the balance law. Under the null energy condition and the asymptotic stationary condition, the entropy is proportional to the area of the apparent horizon up to second-order and satisfies the second law. Without the null energy condition, establishing this area law requires additional assumptions.
ER -