On generalized gravitational entropy, squashed cones and holography

TL;DR

This work demonstrates that the recently proposed squashed-cone regularization, when applied within Fefferman–Graham holography, yields the correct universal entanglement entropy terms for spherical and cylindrical entangling surfaces across a range of higher-derivative gravities. By computing generalized gravitational entropy via the LM prescription and comparing with Wald entropy on the FG background, the authors show consistent results with the Ryu–Takayanagi/Jacobson–Myers frameworks, including in Gauss–Bonnet and related theories. They also derive the entangling-surface equation in Gauss–Bonnet gravity and discuss the connection to Iyer–Wald and Renyi entropy universality, suggesting a broader applicability of Wald-type formalisms in non-Einstein holography. Overall, the paper provides a coherent route to universal EE terms in higher-curvature holography and clarifies the roles of regularization and Noether-charge formalisms in this context.

Abstract

We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universal parts of the entanglement entropy for both spherical and cylindrical entangling surfaces. We comment on the relation with the Iyer-Wald formula for dynamical horizons relating entropy to a Noether charge. Finally we show how to derive the entangling surface equation in Gauss-Bonnet holography.