Local Thermodynamics and Rényi Bounds on Black Hole Mergers
Abstract
Rényi entropy inequalities have been proposed to strengthen the area-theorem bound on mergers of thermodynamically stable black holes in Anti de Sitter (AdS) space. The stronger bounds depend on the joint initial state, whereas masses and temperatures fix only its local thermal marginals. We quantify this distinction inside the canonical two-hole description. Correlations confined to rare energy fluctuations can leave both thermal states exactly intact and drive the trace distance and mutual information to zero, yet still change the joint Rényi entropy at leading semiclassical order. We determine the smallest entropy compatible with a controlled approach to statistical independence, uniformly over all positive Rényi orders up to one. For equal Schwarzschild--AdS4 holes, the resulting optimized canonical mass constraint reduces to the area bound at leading semiclassical order. The reduction concerns only the information needed to infer a bound; it does not produce a lighter attainable remnant or a dynamical instability. Stronger merger constraints therefore require control of the initial correlations beyond single black hole thermodynamics.
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BibTeX
@misc{joshi2026local,
title = {{Local Thermodynamics and Rényi Bounds on Black Hole Mergers}},
author = {Sudhanva Joshi and Sunil Kumar Mishra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31680},
eprint = {2610.31680},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31680},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Local Thermodynamics and Rényi Bounds on Black Hole Mergers
AU - Sudhanva Joshi
AU - Sunil Kumar Mishra
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.31680
UR - https://arxiv.org/abs/2610.31680
AB - Rényi entropy inequalities have been proposed to strengthen the area-theorem bound on mergers of thermodynamically stable black holes in Anti de Sitter (AdS) space. The stronger bounds depend on the joint initial state, whereas masses and temperatures fix only its local thermal marginals. We quantify this distinction inside the canonical two-hole description. Correlations confined to rare energy fluctuations can leave both thermal states exactly intact and drive the trace distance and mutual information to zero, yet still change the joint Rényi entropy at leading semiclassical order. We determine the smallest entropy compatible with a controlled approach to statistical independence, uniformly over all positive Rényi orders up to one. For equal Schwarzschild--AdS_4 holes, the resulting optimized canonical mass constraint reduces to the area bound at leading semiclassical order. The reduction concerns only the information needed to infer a bound; it does not produce a lighter attainable remnant or a dynamical instability. Stronger merger constraints therefore require control of the initial correlations beyond single black hole thermodynamics.
ER -