Reverse Isoperimetry from Boundary--Completed Canonical Energy
Abstract
The reverse isoperimetric conjecture states that, at fixed thermodynamic volume, Schwarzschild--AdS black holes maximize entropy. We show that its local fixed-volume form admits a boundary-completed canonical-energy interpretation. The key observation is that the bulk Hollands--Wald canonical energy vanishes on exact stationary black-hole families, while the fixed-volume entropy Hessian is encoded in an asymptotic boundary contribution. The same structure governs the global comparison. We choose an affine parameterization of a fixed-volume stationary branch connecting Schwarzschild--AdS to the solution of interest. If the stationary boundary Hessian is non-negative along this comparison, entropy concavity gives the reverse isoperimetric bound, while equality is determined by the directions along which the boundary Hessian vanishes. In Einstein gravity this reproduces the area--volume inequality on the stated comparison branches, and the formulation extends naturally to Wald entropy in higher-derivative theories.
Versions
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BibTeX
@misc{kumar2026reverse,
title = {{Reverse Isoperimetry from Boundary--Completed Canonical Energy}},
author = {Naman Kumar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.28427},
eprint = {2606.28427},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.28427},
}
RIS
TY - UNPB
TI - Reverse Isoperimetry from Boundary--Completed Canonical Energy
AU - Naman Kumar
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2606.28427
UR - https://arxiv.org/abs/2606.28427
AB - The reverse isoperimetric conjecture states that, at fixed thermodynamic volume, Schwarzschild--AdS black holes maximize entropy. We show that its local fixed-volume form admits a boundary-completed canonical-energy interpretation. The key observation is that the bulk Hollands--Wald canonical energy vanishes on exact stationary black-hole families, while the fixed-volume entropy Hessian is encoded in an asymptotic boundary contribution. The same structure governs the global comparison. We choose an affine parameterization of a fixed-volume stationary branch connecting Schwarzschild--AdS to the solution of interest. If the stationary boundary Hessian is non-negative along this comparison, entropy concavity gives the reverse isoperimetric bound, while equality is determined by the directions along which the boundary Hessian vanishes. In Einstein gravity this reproduces the area--volume inequality on the stated comparison branches, and the formulation extends naturally to Wald entropy in higher-derivative theories.
ER -