Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Halder, Supratim, Mandlik, Mangesh
Institution: Indian Institute of Technology Dhanbad
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220713018