1999

Ph.D

University of Madras

Black holes are formed when stars with mass around few times the mass of our Sun or higher collapse under their own gravitational field. Black holes are solutions of Einstein's equation which relates space time to matter. This thesis studies the semi-classical approach to quantisation, treating gravity as classical and all other fields are treated as quantum fields. This approach led to the discovery of the phenomenon of black hole radiation. Ordinary thermodynamic systems have a statistical description in terms of microscopic constituents, like a gas having molecules as its microscopic constituents. This thesis precisely addresses the question that Does the black hole have such a description? String theory describes all interactions including gravity in a unified framework and gives a complete theory of the quantum nature of the quantum nature of space time. This thesis studies how the string theory helps in giving a microscopic description of black hole thermodynamics. The aspects of black hole thermodynamics and semi classical gravity including Hawking radiation is reviewed. D-branes, some of the solitonic objects which describe black holes are explained. This thesis also describes anti-de Sitter spaces which helps to understand the properties of certain black holes with the help of a recent conjecture relating physical quantities on anti de Sitter spaces to those of a conformal field theory which lives on its boundary. For certain black holes like the Schwarzschild black hole, the Greybody factor is frequency independent and for low frequencies equals the area of horizon. For these black holes the spectrum is very similar to black body radiation. For certain other black holes, this factor plays a crucial role, which is discussed in this thesis. The researcher studies the back reaction of scalar and fermion matter fields on the black hole geometry, the fields having support on space-like slices very near the horizon. The Schwarzschild black hole is taken for simplicity, found the interactions of the fermionic and scalar outgoing and infalling fields , and shown that they can't be ignored in a derivation of Hawking radiation. The extremal black hole entropy is considered, and seen that the semiclassical derivations suggest that it is zero. For String theory black holes only a very special case of extremal black holes has this feature. The special case is studied and a resolution of the apparant contradiction for those black holes is suggested. Hawking radiation from a black hole in 4 dimensions, obtained by compactifying M theory on T^7. The radiation rate has a structure reproduceable from a 1+1 CFT. Further a microscopic description of fermionic radiation from the D1 D5 black hole is given. The 2+1 dimensional BTZ black hole and fermionic radiation associated with it are discussed. Also discusses the radiation from the 5 dimensional black hole, whose near horizon geometry is the product of 2+1 dimensional BTZ black hole and a compact manifold. The emission rates for scalars, fermions and vectors are determined by probing the near horizon geometry. The thesis concludes with a discussion of the current status of understanding of black hole thermodynamics.