Effect of N=2 Supersymmetric Gauss-Bonnet Term on Black Hole Entropy

Abstract

Black holes are solutions of classical Einstein gravity. They also have information about the quantum nature of the theory of gravity. Thus black holes provide a good laboratory to study some aspects of quantum gravity. In particular, the entropy of black hole is an important property to study. Entropy carries information about the degeneracy of the micro-states associated with a black hole. When the theory gets quantum corrections, the corresponding micro-state degeneracy changes and hence the black hole entropy also changes.

String theory is a promising candidate of quantum gravity. Hence, we study black hole solutions that appear as solutions in string theory. In particular we study supersymmetric and non-supersymmetric black hole solutions in supergravity theory (which is the low energy/classical limit of string theory). We only concentrate on N = 2 supergravity theory. A new class of higher derivative terms has been recently found in this theory. Since these terms appear at higher order in derivatives, they are able to produce quantum effects in the corresponding black hole solutions.

In this thesis, we try to see if a special case of this higher derivative term, known as the Gauss-Bonnet term, affects the entropy of supersymmetric and non-supersymmetric black hole solutions or not. Our results signify that while the term does not change the entropy of supersymmetric black holes, it can potentially change the entropy of non-supersymmetric ones. We further aim to find the exact correction to its entropy.