Wald's entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling

TL;DR

This paper demonstrates that Wald's Noether charge entropy for stationary black holes in general gravity theories equals a quarter of the horizon area when measured with an effective gravitational coupling, extending the Bekenstein-Hawking result.

Contribution

It establishes that Wald's entropy matches a quarter of the horizon area using an effective gravitational coupling, generalizing the classic Bekenstein-Hawking formula.

Findings

Wald's entropy equals a quarter of the horizon area in units of effective gravitational coupling.

Explicit examples of static spherically symmetric black holes confirm the result.

The effective gravitational coupling is defined by the kinetic term coefficient of graviton polarizations.

Abstract

The Bekenstein-Hawking entropy of black holes in Einstein's theory of gravity is equal to a quarter of the horizon area in units of Newton's constant. Wald has proposed that in general theories of gravity the entropy of stationary black holes with bifurcate Killing horizons is a Noether charge which is in general different from the Bekenstein-Hawking entropy. We show that the Noether charge entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling on the horizon defined by the coefficient of the kinetic term of specific graviton polarizations on the horizon. We present several explicit examples of static spherically symmetric black holes.