Extremal black hole

Routing protocol

Entropy (arrow of time)

Quantum gravity

Gravitational collapse

Physics

Gravitation

Euclidean geometry

White hole

Visual arts

Path integral formulation

Angular momentum

Geometry

Replica

Wormhole

Computer network

Theoretical physics

Mathematics

Computer science

Black hole (networking)

Quantum mechanics

Routing (electronic design automation)

Classical mechanics

Rotating black hole

Quantum

Link-state routing protocol

Journal of High Energy Physics

Quantum extremal islands reproduce the unitary Page curve of an evaporating black hole. This has been derived by including replica wormholes in the gravitational path integral, but for the transient, evaporating black holes most relevant to Hawking's paradox, these wormholes have not been analyzed in any detail. In this paper we study replica wormholes for black holes formed by gravitational collapse in Jackiw-Teitelboim gravity, and confirm that they lead to the island rule for the entropy. The main technical challenge is that replica wormholes rely on a Euclidean path integral, while the quantum extremal islands of an evaporating black hole exist only in Lorentzian signature. Furthermore, the Euclidean equations are non-local, so it is unclear how to bridge the gap between the Euclidean path integral and the local, Lorentzian dynamics of an evaporating black hole. We address these issues with Schwinger-Keldysh techniques and show how the non-local equations reduce to the local `boundary particle' description in special cases.

Replica wormholes for an evaporating 2D black hole