Holographic Entanglement Entropy in Time Dependent Gauss-Bonnet Gravity

TL;DR

This paper investigates how holographic entanglement entropy probes penetrate the horizons in Gauss-Bonnet gravity during dynamical processes, revealing that the sign of the coupling significantly affects the depth of the probe.

Contribution

It demonstrates that the entanglement entropy probe's penetration depth varies with the Gauss-Bonnet coupling sign, uncovering new solutions and behaviors near the singularity.

Findings

For positive coupling, less of the horizon is explored than in Einstein gravity.

For negative coupling, new solutions reach close to the singularity.

Probes can explore all the way to the singularity for negative coupling at early times.

Abstract

We study holographic entanglement entropy in Gauss-Bonnet gravity following a global quench. It is known that in dynamical scenarios the entanglement entropy probe penetrates the apparent horizon. The goal of this work is to study how far behind the horizon can the entanglement probe reach in a Gauss-Bonnet theory. We find that the behavior is quite different depending on the sign of the Gauss-Bonnet coupling $\lambda_{GB}$. We show that for $\lambda_{GB} > 0$ the holographic entanglement entropy probe explores less of the spacetime behind the horizon than in Einstein gravity. On the other hand, for $\lambda_{GB} < 0$ the results are strikingly different; for early times a new family of solutions appears. These new solutions reach arbitrarily close to the singularity. We calculate the entanglement entropy for the two family of solutions with negative coupling and find that the ones that reach the singularity are the ones of less entropy. Thus, for $\lambda_{GB} < 0$ the holographic entanglement entropy probes further behind the horizon than in Einstein gravity. In fact, for early times it can explore all the way to the singularity.