Thermodynamics of Black Holes: Semi-Classical Approaches and Beyond

TL;DR

This thesis explores semi-classical black hole thermodynamics, deriving generalized formulas, analyzing Hawking radiation, and classifying phase transitions with novel methods, including higher-order quantum effects and non-commutative gravity influences.

Contribution

It introduces a dimension-independent identity for black hole thermodynamics, computes Hawking radiation spectra considering advanced effects, and proposes a new classification method for black hole phase transitions.

Findings

Derived a generalized Smarr formula for higher-dimensional black holes.

Computed Hawking radiation spectra including quantum and non-commutative effects.

Developed a new methodology to classify black hole phase transitions.

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 $\hbar$) 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.