Entanglement at the Soft-Hair Horizon

TL;DR

This paper investigates quantum entanglement between modes near a supertranslated black hole horizon, revealing how soft hair influences entanglement and mutual information between accelerating observers.

Contribution

It explicitly connects soft hair to near-horizon geometry and quantifies its effect on entanglement measures for bosonic and fermionic fields.

Findings

Entanglement depends on angular position at the soft-hair horizon.

Soft hair modifies entanglement compared to standard Schwarzschild black holes.

Results reduce to Schwarzschild case when soft hair function vanishes.

Abstract

We study entanglement between two modes of a free bosonic and fermionic field as seen by two relatively accelerating observers at the soft-hair horizon of a four-dimensional supertranslated Schwarzschild black hole. First, we associate the shock wave to the near horizon geometry by explicit construction of map between their metric as well as relation between wave form factor and soft hair function. We then compute mutual information and entanglement negativity as a measure of entanglement between these two observers and show that their angular dependence at the soft-hair horizon. We also show that for vanishing soft hair function our results are equal to that of an ordinary Schwarzschild black hole case.