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arXiv · 2608.18583

First Law of Black Hole Interior Dynamics

Ze-Xuan Xiong·H. Lu
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Abstract

We obtain a local first law of dynamics within the interior geometries that are governed by cosmological solutions connecting the event horizon and the Kasner-like singularity. Evaluating the Iyer-Wald identity between the horizon and near-singularity geometries, we define a Kasner potential and transported response coefficients. We test the first law by both exact and numerical solutions. Our formalism provides a self-consistent approach to study the interior dynamics without having to appeal to the outside geometry and the asymptotic charges. It may provide a new approach to study the phase structures of the interior dynamics.

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Ze-Xuan Xiong, H. Lu. 2026-08-19. First Law of Black Hole Interior Dynamics. https://arxiv.org/abs/2608.18583

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