Noether Charge and Black Hole Entropy in Modified Theories of Gravity

TL;DR

This paper investigates black hole entropy in modified gravity theories using the Noether Charge method, showing it remains proportional to horizon area under certain conditions, with specific modifications depending on matter coupling.

Contribution

It extends the Noether Charge approach to various modified gravity theories, clarifying how black hole entropy relates to horizon area and matter coupling.

Findings

Black hole entropy equals one-quarter of horizon area in f(R) theories with conformally invariant matter.

Entropy remains proportional to horizon area even with non-conformal matter, but with different coefficients.

The approach is also applied to dilaton and Ricci tensor-dependent theories, broadening its applicability.

Abstract

The entropy of black holes in modified theories of gravity is examined in the Palatini formalism using the Noether Charge approach. It is shown that, if the gravitational coupling constant is properly identified, the entropy of a black hole is one-quarter of the horizon area in f(R) theories coupled to conformally invariant matter. If matter is present that is not conformally invariant the entropy is still proportional to the area of the black hole, but the coefficient is generally not one-quarter. The entropy of black holes in generalized dilaton theories and in theories with Lagrangians that depend on an arbitrary function of the Ricci tensor are also examined.