This thesis analyses the behaviour of a real massive scalar field in BTZ spacetime, a 2+1-dimensional black hole solution of the Einstein's field equations with a negative cosmological constant. The analysis is performed for a large class of Robin boundary conditions that can be imposed at infinity and we show whether, for a given boundary condition, there exists a ground state by constructing explicitly its two-point function. We demonstrate that, for a subclass of such boundary conditions, it is possible to construct a ground state that locally satisfies the Hadamard property. In all other cases we show that bound state mode solutions exist, a novel feature in literature. Moreover we show that the presence of bound state mode solutions prevents the construction of a physically acceptable ground state. Subsequently we focus our attention in a neighborhood of a Killing horizon in a 2+1-dimensional spacetime, so to analyse the local behaviour of the two-point correlation function of a quantum state for a scalar field. In particular we show that, if the state is of Hadamard form in such neighbourhood, the two-point correlation function exhibits a thermal behaviour at the Hawking temperature, under a suitable scaling limit towards the horizon. This results are then specified to the case of a massive, real scalar field subject to Robin boundary conditions in the the non-extremal, rotating BTZ spacetime.

Hadamard states and tunnelling effects for a BTZ black hole

BUSSOLA, FRANCESCO
2019-01-25

Abstract

This thesis analyses the behaviour of a real massive scalar field in BTZ spacetime, a 2+1-dimensional black hole solution of the Einstein's field equations with a negative cosmological constant. The analysis is performed for a large class of Robin boundary conditions that can be imposed at infinity and we show whether, for a given boundary condition, there exists a ground state by constructing explicitly its two-point function. We demonstrate that, for a subclass of such boundary conditions, it is possible to construct a ground state that locally satisfies the Hadamard property. In all other cases we show that bound state mode solutions exist, a novel feature in literature. Moreover we show that the presence of bound state mode solutions prevents the construction of a physically acceptable ground state. Subsequently we focus our attention in a neighborhood of a Killing horizon in a 2+1-dimensional spacetime, so to analyse the local behaviour of the two-point correlation function of a quantum state for a scalar field. In particular we show that, if the state is of Hadamard form in such neighbourhood, the two-point correlation function exhibits a thermal behaviour at the Hawking temperature, under a suitable scaling limit towards the horizon. This results are then specified to the case of a massive, real scalar field subject to Robin boundary conditions in the the non-extremal, rotating BTZ spacetime.
25-gen-2019
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1244306
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