The large D black hole Membrane Paradigm at first subleading order

TL;DR

This paper extends the black hole membrane paradigm in the large D limit to include first subleading order corrections, providing a systematic method and confirming results with quasinormal mode calculations.

Contribution

It introduces a systematic approach to derive higher-order corrections to the membrane equations in the large D expansion, including novel effects like nonzero divergence of membrane velocity.

Findings

Derived first subleading corrections to membrane equations

Identified a new effect: nonzero divergence proportional to shear squared

Matched corrected quasinormal mode frequencies with previous gravitational calculations

Abstract

In the large D limit, and under certain circumstances, it has recently been demonstrated that black hole dynamics in asymptotically flat spacetime reduces to the dynamics of a non gravitational membrane propagating in flat D dimensional spacetime. We demonstrate that this correspondence extends to all orders in a 1/D expansion and outline a systematic method for deriving the corrected membrane equation in a power series expansion in 1/D. As an illustration of our method we determine the first subleading corrections to the membrane equations of motion. A qualitatively new effect at this order is that the divergence of the membrane velocity is nonzero and proportional to the square of the shear tensor reminiscent of the entropy current of hydrodynamics. As a test, we use our modified membrane equations to compute the corrections to frequencies of light quasinormal modes about the Schwarzschild black hole and find a perfect match with earlier computations performed directly in the gravitational bulk.