On holographic entanglement entropy of Horndeski black holes

TL;DR

This paper derives a holographic entanglement entropy functional for Horndeski gravity, clarifies discrepancies in black hole thermal entropy, and explores minimal surfaces and entanglement plateaux.

Contribution

It introduces a new entanglement entropy functional for Horndeski gravity and resolves existing puzzles about black hole entropy in this context.

Findings

Derived the entanglement entropy functional using the squashed cone method.

Identified the minimal surface that evaluates the entanglement entropy.

Clarified the relation between entanglement entropy and black hole thermal entropy.

Abstract

We study entanglement entropy in a particular tensor-scalar theory: Horndeski gravity. Our goal is two-fold: investigate the Lewkowycz-Maldacena proposal for entanglement entropy in the presence of a tensor-scalar coupling and address a puzzle existing in the literature regarding the thermal entropy of asymptotically AdS Horndeski black holes. Using the squashed cone method, i.e. turning on a conical singularity in the bulk, we derive the functional for entanglement entropy in Horndeski gravity. We analyze the divergence structure of the bulk equation of motion. Demanding that the leading divergence of the transverse component of the equation of motion vanishes we identify the surface where to evaluate the entanglement functional. We show that the surface obtained is precisely the one that minimizes said functional. By evaluating the entanglement entropy functional on the horizon we obtain the thermal entropy for Horndeski black holes; this result clarifies discrepancies in the literature. As an application of the functional derived we find the minimal surfaces numerically and study the entanglement plateaux.