Generalized Entropy in Higher Curvature Gravity And Entropy of Algebra of Observables

TL;DR

This paper extends the concept of generalized entropy and the generalized second law from semiclassical Einstein gravity to arbitrary diffeomorphism invariant theories of gravity, linking black hole entropy to algebraic structures of quantum observables.

Contribution

It generalizes the relation between generalized entropy and algebraic quantum observables to a broad class of gravity theories beyond Einstein's, establishing a generalized second law.

Findings

Generalized entropy equals algebraic entropy in arbitrary theories.

Derived a version of the Generalized Second Law for these theories.

Extended the algebraic approach to quantum observables in black hole spacetimes.

Abstract

Recently, Chandrasekaran, Penington and Witten (CPW) have shown that the generalized entropy of the Schwarzschild black hole at the bifurcation surface equals the entropy of an extended von Neumann algebra of quantum observables in the black hole exterior, in semiclassical Einstein gravity. They also derive a version of the Generalized Second law. We generalize these results to a static black hole in an arbitrary diffeomorphism invariant theory of gravity. Thus, a version of the Generalized second law for an arbitrary diffeomorphism invariant theory of gravity follows.