A local second law for black hole dynamics in the charged large D membrane paradigm
Abstract
The large D membrane paradigm provides a perturbative, non-gravitational description of black hole dynamics. While the local second law of thermodynamics has been established for neutral membranes, the explicit determination of the local entropy production in the charged large D membrane paradigm remains an open problem. In this paper, we compute the subleading-order correction to the divergence of the membrane velocity for a charged black hole in a flat background. Using the non-affine null Raychaudhuri equation and the Einstein-Maxwell equation at the physical event horizon, we relate the horizon expansion to the auxiliary membrane kinematics. We demonstrate that the membrane velocity produces a non-negative divergence at the first non-vanishing order in the membrane worldvolume, which is driven by two quadratic forms: the membrane shear and an additional term arising from the Maxwell field. Using this result, we subsequently construct the corresponding membrane entropy current and establish the non-negativity of its divergence through this order, thereby establishing the local second law for the charged large D membrane paradigm.
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BibTeX
@misc{halder2026local,
title = {{A local second law for black hole dynamics in the charged large $D$ membrane paradigm}},
author = {Supratim Halder and Mangesh Mandlik},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06470},
eprint = {2610.06470},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06470},
}
RIS
TY - UNPB
TI - A local second law for black hole dynamics in the charged large D membrane paradigm
AU - Supratim Halder
AU - Mangesh Mandlik
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.06470
UR - https://arxiv.org/abs/2610.06470
AB - The large D membrane paradigm provides a perturbative, non-gravitational description of black hole dynamics. While the local second law of thermodynamics has been established for neutral membranes, the explicit determination of the local entropy production in the charged large D membrane paradigm remains an open problem. In this paper, we compute the subleading-order correction to the divergence of the membrane velocity for a charged black hole in a flat background. Using the non-affine null Raychaudhuri equation and the Einstein-Maxwell equation at the physical event horizon, we relate the horizon expansion to the auxiliary membrane kinematics. We demonstrate that the membrane velocity produces a non-negative divergence at the first non-vanishing order in the membrane worldvolume, which is driven by two quadratic forms: the membrane shear and an additional term arising from the Maxwell field. Using this result, we subsequently construct the corresponding membrane entropy current and establish the non-negativity of its divergence through this order, thereby establishing the local second law for the charged large D membrane paradigm.
ER -