The Black Hole Membrane Paradigm in f(R) Gravity

TL;DR

This paper extends the black hole membrane paradigm to f(R) gravity theories, deriving the fluid-like properties of horizons and analyzing their thermodynamics, revealing non-Newtonian behavior except in Einstein gravity.

Contribution

It generalizes the membrane paradigm to f(R) gravity, deriving stress tensors and transport coefficients for black hole horizons in these theories.

Findings

Membrane behaves as a non-Newtonian fluid in f(R) gravity.

In Einstein gravity, the membrane exhibits Newtonian fluid behavior.

Thermodynamic properties of the membrane are analyzed using Euclidean methods.

Abstract

To an outside observer, a black hole's event horizon appears to behave exactly like a dynamical fluid membrane. We extend this membrane paradigm to black holes in general $f(R)$ theories of gravity. We derive the stress tensor and various transport coefficients of the fluid and find that the membrane behaves as a non-Newtonian fluid except for the special case of Einstein gravity. Using Euclidean methods, we study the thermodynamics of the membrane. We speculate on what theories of gravity admit horizons with fluid properties.