Notes on Derivation of 'Generalized Gravitational Entropy'

TL;DR

This paper presents a new derivation of generalized gravitational entropy for entangling surfaces, avoiding conical singularities and confirming that these surfaces are extrema of the entropy functional, aligning with previous results in Lovelock gravity.

Contribution

It introduces an alternative derivation method for gravitational entropy that simplifies calculations and confirms the extremal nature of entangling surfaces in Lovelock theories.

Findings

Derivation method avoids conical singularities

Entangling surfaces are extrema of the entropy functional

Results agree with previous Lovelock gravity calculations

Abstract

An alternative derivation of generalized gravitational entropy associated to co-dimension 2 'entangling' hypersurfaces is given. The approach is similar to the Jacobson-Myers 'Hamiltonian' method and it does not require computations on manifolds with conical singularities. It is demonstrated that the entangling surfaces should be extrema of the entropy functional. When our approach is applied to Lovelock theories of gravity the generalized entropy formula coincides with results derived by other methods.