Tunnelling processes for Hadamard states through a 2+1 dimensional black hole and Hawking radiation

We analyse the local behaviour of the two-point correlation function of a quantum state for a scalar field in a neighbourhood of a Killing horizon in a \(2+1\)-dimensional spacetime, extending the work of Moretti and Pinamonti in a \(3+1\)-dimensional scenario. In particular we show that, if the sta...

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Bibliographic Details
Published in:arXiv.org 2018-06
Main Authors: Bussola, Francesco, Dappiaggi, Claudio
Format: Article
Language:English
Subjects:
Black holes
Boundary conditions
Hawking radiation
Horizon
Spacetime
Thermodynamic properties
Online Access:Get full text
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Summary:We analyse the local behaviour of the two-point correlation function of a quantum state for a scalar field in a neighbourhood of a Killing horizon in a \(2+1\)-dimensional spacetime, extending the work of Moretti and Pinamonti in a \(3+1\)-dimensional scenario. In particular we show that, if the state is of Hadamard form in such neighbourhood, similarly to the \(3+1\)-dimensional case, under a suitable scaling limit towards the horizon, the two-point correlation function exhibits a thermal behaviour at the Hawking temperature. Since the whole analysis rests on the assumption that a Hadamard state exists in a neighbourhood of the Killing horizon, we show that this is not an empty condition by verifying it for a massive, real scalar field subject to Robin boundary conditions in the prototypic example of a three dimensional black hole background: the non-extremal, rotating BTZ spacetime.
ISSN:2331-8422
DOI:10.48550/arxiv.1806.00427