Islands with Gravitating Baths: Towards ER = EPR

TL;DR

This paper explores the connection between entanglement and wormhole geometry in black hole models with gravitating baths, providing evidence for the ER=EPR conjecture through various models and transitions.

Contribution

It introduces new models of entangled black holes in JT gravity demonstrating ER=EPR and analyzes entanglement-induced geometric transitions.

Findings

Entanglement induces a Hawking-Page-like transition to a connected wormhole geometry.

Models show similar entanglement entropy behavior to non-gravitating baths.

Discussion of dynamical transitions potentially realizing ER=EPR in evolving black holes.

Abstract

We study the Page curve and the island rule for black holes evaporating into gravitating baths, with an eye towards establishing a connection with the ER=EPR proposal. We consider several models of two entangled 2d black holes in Jackiw-Teitelboim (JT) gravity with negative cosmological constant. The first, "doubled PSSY," model is one in which the black holes have end-of-the-world (ETW) branes with a flavour degree of freedom. We study highly entangled states of this flavour degree of freedom and find an entanglement-induced Hawking-Page-like transition from a geometry with two disconnected black holes to one with a pair of black holes connected by a wormhole, thus realising the ER = EPR proposal. The second model is a dynamical one in which the ETW branes do not have internal degrees of freedom but the JT gravity is coupled to a 2d CFT, and we entangle the black holes by coupling the two CFTs at the $AdS$ boundary and evolving for a long time. We study the entanglement entropy between the two black holes and find that the story is substantially similar to that with a non-gravitating thermal bath. In the third model, we couple the two ends of a two-sided eternal black hole and evolve for a long time. Finally, we discuss the possibility of a Hawking-Page-like transition induced by real-time evolution that realises the ER = EPR proposal in this dynamical setting.