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.
Description
Replica wormholes for an evaporating 2D black hole
%0 Generic
%1 goto2020replica
%A Goto, Kanato
%A Hartman, Thomas
%A Tajdini, Amirhossein
%D 2020
%K arxiv
%T Replica wormholes for an evaporating 2D black hole
%U http://arxiv.org/abs/2011.09043
%X 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.
@misc{goto2020replica,
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 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.},
added-at = {2020-11-21T00:05:37.000+0100},
author = {Goto, Kanato and Hartman, Thomas and Tajdini, Amirhossein},
biburl = {https://www.bibsonomy.org/bibtex/2b1c01aaff45bd1e335bd222d81ffffee/nimaaj},
description = {Replica wormholes for an evaporating 2D black hole},
interhash = {ed341ad8b3c061a55277d4e6f98636d3},
intrahash = {b1c01aaff45bd1e335bd222d81ffffee},
keywords = {arxiv},
note = {cite arxiv:2011.09043Comment: 65 pages, 19 figures},
timestamp = {2020-11-21T00:05:37.000+0100},
title = {Replica wormholes for an evaporating 2D black hole},
url = {http://arxiv.org/abs/2011.09043},
year = 2020
}