Upper bounds of holographic entanglement entropy growth rate for thermofield double states

TL;DR

This paper investigates the maximum possible rate at which entanglement entropy can grow in holographic systems, establishing bounds based on black hole geometries and energy conditions, with implications for understanding quantum information dynamics in gravity.

Contribution

It conjectures and proves that vacuum AdS black holes maximize entanglement entropy growth rate among static black holes of the same mass or entropy, considering various energy conditions.

Findings

Vacuum AdS black holes have the highest entropy growth rate under certain conditions.

Scalar fields violating energy conditions can still lead to maximal growth rates when fixing entropy.

Maximal growth rate depends on the quantization scheme when fixing energy.

Abstract

We studied the upper bounds of the holographic entanglement entropy growth rate for thermofield double (TFD) states. By comparing the cases of vacuum AdS and charged AdS black holes, we conjecture: for all static planar or spherically symmetric asymptotically Schwarzschild-AdS black holes of same mass density or entropy density, the vacuum AdS black hole gives the maximum entanglement entropy growth rate. We gave proofs by assuming dominant energy condition. We also considered the AdS black hole spacetime with real scalar fields case, where the scalar fields violate the dominant energy condition and the bulk geometry is not asymptotically Schwarzschild-AdS. Numerical results show that this case vacuum black hole still has maximal growth rate if we fixed entropy. However, in the case of fixed energy, vacuum case has maximal growth rate of entanglement entropy only under standard quantization scheme.