Entanglement between two evaporating black holes

TL;DR

This paper investigates the entanglement properties of two black holes in different universes, exploring how their spacetime geometries can be glued together and how this affects entanglement entropy calculations.

Contribution

It introduces a method to construct glued spacetimes for entanglement entropy computation in various asymptotic geometries, including cases with unequal black hole masses.

Findings

Spacetime gluing rules are clarified for asymptotically flat and AdS cases.

The entanglement entropy is computed via generalized entropy on the glued spacetime.

The approach extends to more general settings from the gravitational path integral perspective.

Abstract

We study a thermo-field double type entangle state on two disjoint gravitating universes, say A and B, with an eternal black hole on each. As was shown previously, its entanglement entropy of the universe A is computed by the generalized entropy on a new spacetime constructed by suitably gluing the black holes on A and B. We study such spacetime gluings when universes are asymptotically flat and AdS cases, especially when the masses of these black holes are different. We also clarify the rule to construct such a glued spacetime in more general settings from the gravitational path integral view point.