On holographic entanglement entropy of Horndeski black holes
arXiv:1707.06322 · doi:10.1007/JHEP10(2017)145
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.
29 pages, multiple figures. v3: sections 3.2, 3.3 and 4 sharpened
References in corpus (9)
- Causality & holographic entanglement entropy
- supersymmetric indices and the four-dimensional A-model
- A holographic proof of the strong subadditivity of entanglement entropy
- Black holes with non-minimal derivative coupling
- On Holographic Entanglement Entropy and Higher Curvature Gravity
- On entanglement entropy functionals in higher derivative gravity theories
- Building a Holographic Superconductor with a Scalar Field Coupled Kinematically to Einstein Tensor
- Generalized gravitational entropy without replica symmetry
- Horndeski Gravity and the Violation of Reverse Isoperimetric Inequality