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.
Tunnelling processes for Hadamard states through a 2+1 dimensional black hole and Hawking radiation
Bussola, Francesco;Dappiaggi, Claudio
2019-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
