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arXiv · 2605.07236

Large black holes at a finite distance: Quasi-local restricted phase space formalism

Bai-Hao Huang·Liu Zhao
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Abstract

We extend the restricted phase space formalism for spherically symmetric black hole solutions of Einstein-Maxwell theory to the quasi-local regime, with the static observers located at a finite radial distance. The first law and Euler relation for the RN and RN-AdS black holes are proved to hold, but only with the inclusion of an extra pair of thermodynamic variables, {\em i.e.} the pressure $P$ and the area $A$ of the codimension-2 hypersurface on which the observers reside. For the RN black holes, the quasi-local behavior is analyzed in detail. It turns out that the RN black holes in the quasi-local description behaves significantly different from itself in the asymptotic description, but is extremely similar to the RN-AdS black holes in the asymptotic description, {\em e.g.} allowing for isocharge temperature-entropy phase transitions and lack of isovoltage temperature-entropy phase transitions. In the neutral limit, the Hawking-Page-like transitions appear in the quasi-local description which is absent in the asymptotic description. The quasi-local behavior of RN-AdS black holes is also briefly discussed, which is qualitatively identical to the asymptotic description with only quantitative differences.

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Bai-Hao Huang, Liu Zhao. 2026-05-08. Large black holes at a finite distance: Quasi-local restricted phase space formalism. https://arxiv.org/abs/2605.07236

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