Holographic entanglement entropy in time dependent Gauss-Bonnet gravity

Abstract

Abstract We investigate 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 λGB. For λGB > 0 the behavior of the probes is just as in Einstein gravity; the probes do not reach the singularity but asymptote to a locus behind the apparent horizon. We calculate the minimum radial position rmin reached by the probes and show that for λGB > 0 they explore less of the spacetime behind the horizon than in Einstein gravity. On the other hand, for λGB < 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 λGB < 0 and find that the ones that reach the singularity are the ones of less entanglement entropy. Thus, for λGB < 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.

Keywords

• AdS-CFT Correspondence
• Gauge-gravity correspondence