2013

Ph.D

HBNI

Theme of Thesis: One of the significant successes of string theory as a quantum theory of gravity is that it can give a statistical description of the thermodynamic black hole entropy via microstate counting and a macroscopic description via the attractor mechanism. The author explores both the descriptions. The counting of certain class of BPS states in string theory is studied in the microscopic side. A possible generalisation of the attractor mechanism suitable for extremal black brane horizons in gauged supergravity, is studied in the macroscopic side. Generalised attractors in gauged supergravity is constructed and their stability is investigated. Chapter 1, gives a discussion in the basics of string theory and the recent developments. Chapter 2, discusses black hole microstate counting in string theory. String theory has successfully given a statistical understanding of the thermodynamic Bekenstein-Hawking area law by counting microscopic degrees of freedom of certain supersymmetric extremal black holes [2]. Attractor mechanism in supergravity is studied in chapter 3. The independence of the Bekenstein-Hawking entropy of extremal black holes from the asymptotic values of moduli fields is explained by the attractor mechanism. Chapter 4, discusses black holes in AdS space, black brane limits and the Bianchi classification of five dimensional homogeneous extremal black brane horizons [7]. Chapter 5, describes the background material in gauged supergravity. Gauged supergravities are supersymmetry preserving deformations of ungauged supergravity. The deformations are implemented by promoting some of the global symmetries of the ungauged theory to local symmetries. In Chapter 6, the generalised attractors are studied in gauged supergravity and explicit examples of Bianchi attractors from specific models are constructed. A simple gauged supergravity model [18,19] with one vector multiplet is considered for discussion and constructed some explicit examples of such Bianchi attractors. In particular, constructed a "z = 3 Lifshitz solution", Bianchi type II and Bianchi Type VI solutions and argued that Bianchi type III and type V geometries do not exist in the model considered. In [20], different gauged supergravity models, including models in the hypermultiplet sector are explored to embed all the Bianchi type metrics in gauged supergravity. In Chapter 7, the stability of generalised attractors are discussed. The result of the stability analysis [21] is reported in the thesis. This thesis, focussed on the microscopic state counting in string theory and a generalisation of the attractor mechanism to gauged supergravity. Chapter 8 concludes and discusses the future directions.