# Quantum Fields on BTZ Black Holes

Ortiz Hernandez, Leonardo (2011) Quantum Fields on BTZ Black Holes. PhD thesis, University of York.

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In this thesis we investigate some aspects of Quantum Fields on BTZ black holes in 1+1 and 1+2 dimensions. More specifically, we study how a ground state in AdS spacetime becomes a thermal state when restricted to the exterior region of the BTZ black hole. This ground state is for the quantum linear real scalar field which satisfies the Klein-Gordon equation and also, in the 1+2 dimensional case, for a general QFT satisfying the axioms of Algebraic Quantum Field Theory in Curved Spacetime. We also study how these states map to states on the conformal boundary of AdS spacetime. In order to do this we use Algebraic Holography, Boundary-limit Holography and Pre-Holography. As a preparation, we give an exposition of AdS spacetime, we review the principal aspects of the 1+1 and 1+2 dimensional BTZ black holes and their mapping to the boundary of AdS spacetime. In both cases they map to part of the boundary of AdS spacetime. In the 1+1 case we find that the restriction of the equivalent global vacuum or the Poincar\'{e} vacuum on the boundary becomes a thermal state (KMS state) when restricted to the BTZ black hole. In the 1+2 case we find that the Poincar\'{e} vacuum becomes a thermal state too when restricted to the exterior of the BTZ black hole. In both cases the temperature of the state is $\textsf{T}=\frac{\kappa}{2\pi}$, where $\kappa$ is the surface gravity. In 1+2 dimensions we give as a concrete model the quantum linear real scalar field. When we study these states in the boundary of AdS spacetime we use standard techniques of Conformal Field Theory. One of the main conclusions we get from our investigation is that in certain sense the Hawking effect in the eternal BTZ black hole maps to the Unruh effect on the boundary of AdS spacetime. In the final part of this thesis we study the brick wall model for these black holes for the quantum linear real scalar field. In both cases we obtain the two point function for the vacuum and thermal states in the bulk and on the boundary. We also study the expectation value of the renormalized energy-momentum tensor in 1+1 dimensions for the conformal massless quantum real scalar field. Most of this thesis fits in the framework of AdS/CFT in QFT which is more limited than AdS/CFT correspondence in string theory.