Thermodynamics of Black Holes: Semi-Classical Approaches and Beyond

Abstract

This thesis is focussed to study various aspects of black hole physics. Our approach is a semi-classical type, where the spacetime geometry of black holes is considered to be classical but the fields moving in the background are quantum in nature. Some notable facets of this thesis are the following. We start by looking into the issue of generalized Smarr mass formula for arbitrary dimensional black holes in Einstein-Maxwell gravity. We derive this formula for these black holes and also demonstrate that such a formula can be expressed in the form of a dimension independent identity $K_{{\chi }^{\mu }}=2ST$ (where the l.h.s is the Komar conserved charge corresponding to the null Killing vector ${\chi }^{\mu }$ and in the r.h.s $S,T$ are the semi-classical entropy and temperature of a black hole) defined at the black hole event horizon. We highlight the role of exact differentials in computations involving black hole thermodynamics. Some results like the first law of black hole thermodynamics and semi-classical entropy are obtained without using the laws of black hole mechanics as usually done. The blackbody (Hawking) radiation spectrum for higher dimensional black holes is computed by using a density matrix technique of tunneling mechanism by considering both event and cosmological horizons. We also provide the modifications to the semi-classical Hawking temperature and Bekenstein-Hawking entropy due to various effects. These modifications are mainly found due to higher order (in $\hslash$) effects to the WKB ansatz used for the quantum tunneling formalism and non-commutative gravity inspired effects. Finally, in we discuss phase transition phenomena in black holes. We formulate a new methodology based on Clausius-Clapeyron and Ehrenfest's equations to exhibit and classify phase transitions in black holes in analogy to what is done in standard thermodynamics.

Ph.D. thesis, 152 pages (including the front matter) ; Supervisor: Rabin Banerjee ; Institution: S.N. Bose National Centre for Basic Sciences, Kolkata, India ; Degree awarded on August 24, 2012 from University of Calcutta, Kolkata, India

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• Charged Fermions Tunnelling from Kerr-Newman Black Holes
• Noncommutative Black Hole Thermodynamics
• Anomalies, Hawking Radiations and Regularity in Rotating Black Holes
• Non-commutative geometry inspired higher-dimensional charged, black holes
• Temporal contribution to gravitational WKB-like calculations
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• Subtleties in the quasi-classical calculation of Hawking radiation
• Fermion Tunneling from Dynamical Horizons
• Black hole quantum tunnelling and black hole entropy correction
• Fermion Tunneling Beyond Semiclassical Approximation
• Quantum Tunneling and Trace Anomaly
• Hawking temperature from tunnelling formalism
• Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
• Corrected entropy of BTZ black hole in tunneling approach
• Hawking radiation of Dirac particles via tunneling from Kerr black hole
• Hawking Radiation and Covariant Anomalies
• Dirac particles' tunnelling from black rings
• Thermodynamics and phase transitions in the Born-Infeld-anti-de Sitter black holes
• Hawking Radiation from General Kerr-(anti)de Sitter Black Holes
• Rotating Black Holes in Higher Dimensional Einstein-Maxwell Gravity
• Exact Differential and Corrected Area Law for Stationary Black Holes in Tunneling Method
• Black Hole Thermodynamics and the Factor of 2 Problem
• Hawking Radiation, Effective Actions and Covariant Boundary Conditions
• Self-sustained traversable wormholes in noncommutative geometry
• Noncommutative Schwarzschild Black Hole and Area Law
• Statistical Origin of Gravity
• Deformed Reissner--Nordstrom solutions in noncommutative gravity
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