Membrane paradigm of black holes in Chern-Simons modified gravity

TL;DR

This paper explores the membrane paradigm of black holes within Chern-Simons modified gravity, revealing a complex stress tensor structure and fluid-like equations applicable to static black hole solutions.

Contribution

It derives the membrane stress tensor from the action principle in Chern-Simons gravity and demonstrates its fluid-like behavior in static black hole geometries.

Findings

Membrane stress tensor exhibits rich structure due to Chern-Simons term

Membrane obeys fluid continuity and Navier-Stokes equations under certain conditions

Schwarzschild black hole solution fits within this modified membrane paradigm

Abstract

The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.