Holographic actions from black hole entropy

TL;DR

This paper presents a method to derive higher-order effective gravitational actions from black hole entropy, focusing on f(R) theories and incorporating quantum corrections, linking entropy with fundamental action principles.

Contribution

It introduces a novel approach to obtain effective actions directly from black hole entropy, emphasizing the emergent nature of gravity and extending to quantum-corrected entropy models.

Findings

Derived higher-order effective actions from entropy

Applied method to f(R) theories and quantum corrections

Linked black hole entropy with fundamental gravitational actions

Abstract

Using the Wald's relation between the Noether charge of diffeomorphisms and the entropy for a generic spacetime possessing a bifurcation surface, we introduce a method to obtain a family of higher order derivatives effective actions from the entropy of black holes. Our point of view is to consider fundamental the black hole entropy and the action an emerged object. We then specialize to a particular class of effective theories: the f(R) theories. We apply the idea, using a simple mind ansatz, to loop quantum gravity and to a general class of log-corrected entropy formulas.