Abstract
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 for the Schwarzian mode are non-local, so it is unclear how to connect to 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.
Highlights
The entropy of Hawking radiation is a diagnostic of information loss
The entropy was calculated in the low-energy theory by Almheiri, Engelhardt, Marolf and Maxfield [1] and simultaneously by Penington [2] using an extension of the gravitational entropy formula [1,2,3,4,5,6,7,8]
We are primarily interested in the Page curve for the black hole in figure 1
Summary
The entropy of Hawking radiation is a diagnostic of information loss. It was long believed that this entropy could only be computed in the ultraviolet theory. Derivations of gravitational entropy from the replica method, this is on a similar conceptual footing to the Gibbons-Hawking derivation of the area law — it computes the entropy without telling us what microstates are responsible, or whether such microstates really exist This example illustrates some conceptual points that are hidden in the derivation of the island rule based on the action [13, 14], such as the role of conformal welding, the relation between the local analysis [5] and the Schwarzian theory, and other subtleties that arise in Lorentzian signature. (See section 5.1.) The derivation applies to any state in this theory created by a Euclidean path integral with local operator insertions, generalizing the eternal black hole analysis in [13]. In the rest of this introduction, we describe our setup in more detail, highlight some technical challenges, and summarize how things unfold
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
