Thermodynamics of Black Holes: Semi-Classical Approaches and Beyond
Sujoy Kumar Modak
备注：
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
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 $K_{χ^μ}=2ST$ (where the l.h.s is the Komar conserved charge corresponding to the null Killing vector $χ^μ$ 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.
Black holes have often provided profound insights into the nature of gravity and the structure of space-time. The study of the mathematical properties of black objects is a major research theme of contemporary theoretical physics. This review presents a comprehensive survey of the various versions of the first law and second law of black hole mechanics in general relativity and beyond. The emphasis is to understand how these laws can constrain the physics beyond general relativity.
We study the thermodynamics of accelerating asymptotically AdS black holes with scalar hair in four-dimensional Einstein-Maxwell-dilaton theories, which can be embedded in gauged supergravities for specific dilaton coupling constants. These accelerating black holes are described by charged dilaton C metrics, which have unique features but are almost unexplored before. Thermodynamics of slowly accelerating black holes is generalized to include scalar hair. We find that properly accounting for mixed boundary conditions for the scalar field leads to standard consistent first law and other thermod…
Thermodynamics of Constant Curvature Black Holes Through Semi-Classical Tunneling
本文研究了常曲率黑洞视界中标量场和费米子场的半经典隧穿，该黑洞是局部AdS，其五维类似物是${\cal N}=4$ Super Yang-Mills的对偶.特别是，我们强调的强烈依赖的隧道方法霍金辐射的近视界对称性，一个事实往往隐藏在背后的算法程序，隧道的方法往往被使用。我们最终计算出标量和费米子的发射率，从而计算出黑洞的霍金温度。
Quantum extremal surfaces (QES), codimension-2 spacelike regions which extremize the generalized entropy of a gravity-matter system, play a key role in the study of the black hole information problem. The thermodynamics of QESs, however, has been largely unexplored, as a proper interpretation requires a detailed understanding of backreaction due to quantum fields. We investigate this problem in semi-classical Jackiw-Teitelboim (JT) gravity, where the spacetime is the eternal two-dimensional Anti-de Sitter ($\text{AdS}_{2}$) black hole, Hawking radiation is described by a conformal field theory…
In the extended phase space approach, one can define thermodynamic pressure and volume that gives rise to the van der Waals type phase transition for black holes. For Einstein's GR, the expressions of these quantities are unanimously accepted. Of late, the van der Waals phase transition in black holes has been found in modified theories of gravity as well, such as the $f(R)$ gravity and the scalar-tensor gravity. However, in the case of these modified theories of gravity, the expression of pressure (and, hence, volume) is not uniquely determined. In addition, for these modified theories, the e…
The first and second laws of black hole thermodynamics are verified to emerge from a generic semiclassical theory of gravity for which a Hamiltonian can be defined. The first law is established for stationary spacetimes, and the second law is established in the here defined "piecewise stationary" spacetimes. Black hole entropy is defined in the Noether charge approach, and the entropy for the matter in its exterior is the von Neumann entropy of the quantum fields. These results strongly support the view of black hole entropy as an account of the information that is hidden behind the horizon.
Beyond Comoving Volume: Horizon Flux and Matter Creation in Modified Cosmology from the Unified First Law of Thermodynamics
Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso（瓦尔帕莱索大学科学与物理天文学研究所）；Facultad de Física, Universidad Veracruzana（韦拉克鲁斯大学物理学院）；Instituto de Física, Pontificia Universidad Católica de Valparaíso（瓦尔帕莱索天主教大学物理研究所）
Entropy applications in cosmology: spacetime thermodynamics, holographic dark energy, entropic gravity and beyond - a review
National Observatory of Athens（雅典国家天文台）；University of Science and Technology of China（中国科学技术大学）；Universidad Católica del Norte（北方天主教大学）；University of Lleida（莱里达大学）；University of Patras（帕特雷大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；University of Waterloo（滑铁卢大学）
Based on semiclassical tunneling method, we focus on charged fermions tunneling from higher-dimensional Reissner-Nordström black hole. We first simplify the Dirac equation by semiclassical approximation, and then a semiclassical Hamilton-Jacobi equation is obtained. Using the Hamilton-Jacobi equation, we study the Hawking temperature and fermions tunneling rate at the event horizon of the higher-dimensional Reissner-Nordström black hole spacetime. Finally, the correct entropy is calculation by the method beyond semiclassical approximation.
This paper comprehensively explores Stephen Hawking's interaction with Jacob Bekenstein. Both Hawking and Bekenstein benefited from the interaction with each other. It is shown that Hawking's interaction with Bekenstein drove him to solve the problems in Bekenstein's black hole thermodynamics in terms of a new thermal radiation mechanism. Hawking derived the thermal radiation using a semiclassical approximation in which the matter fields are treated quantum mechanically on a classical spacetime background. Hawking's semiclassical approximation yielded a simple formula for the entropy of the bl…
