Aspects of Black holes in Anti-deSitter Space

Abstract

Some aspects of black holes in Anti deSitter Space times are studied in this thesis. A semi classical analysis of black holes shows that they also radiate with a thermal spectrum. This together with the fact that black holes obey laws that are similar to the laws of thermodynamics, implies that the laws of black hole mechanics could be thought of laws of thermodynamics of black holes, where certain quantities associated with black holes could be identified with standard thermodynamic quantities. The BTZ black hole offers an arena for studying the origin of the states accounting for the semi-classical entropy and of the next order correction which also seems to be universal. The BTZ black hole is viewed in different formulations of Euclidean gravity in three dimensions. The correction to the Bekenstein-Hawking entropy for the Lorentzian BTZ black hole has been computed by studying the Cardy formula for the growth of states of the asymptotic conformal field theory at the boundary of the black hole spacetime. An exact expression for the partition function of the BTZ blackhole is derived in the Euclidean path integral approach. The computation uses the formulation of three dimensional gravity with a negative cosmological constant in terms of Chern-Simons theory. It is found that in the context of the BTZ black hole the right expression for the logarithmic correction comes from the modular invariance associated with the total boundary of the black hole. Also the BTZ black hole is examined in the Ponzano-Regge-Turaev-Viro(PRTV) Euclidean lattice gravity formulation; And described in this formulation and, on considering all possible triangulations of the BTZ black hole, keeping the horizon length fixed, the semiclassical Bekenstein-Hawking entropy is reproduced. The maximum contribution to the entropy comes from states at the horizon. The next order corrections to the entropy in this formulation also commented. A novel method is proposed, based on the superpotentials for obtaining the quasi normal modes of AdS black holes. The lowest quasi-normal mode of the 2+1 dimensional BTZ black hole is obtained exactly; The modes are proportional to the surface gravity of the black hole. The study proposes a scheme by which the potential corresponding to a scalar field perturbation of any AdS black hole can be approximated by a potential series derived from a superpotential. This is used to compute the quasi-normal modes of the five dimensional AdS Schwarzschild black hole.