Quantum Fields on BTZ Black Holes

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.