Quantum Tunneling in Black Holes

Abstract

This thesis is focussed towards the applications of the quantum tunneling mechanism to study black holes. Here we give a general frame work of the existing tunneling mechanism, both the radial null geodesic and Hamilton Jacobi methods. On the radial null geodesic method side, we study the modifications to the tunneling rate, Hawking temperature and the Bekenstein- Hawking area law by including the back reaction as well as non-commutative effects in the space-time. A reformulation of the Hamilton-Jacobi (HJ) method is first introduced. Based on this, a close connection between the quantum tunneling and the gravitational anomaly mechanisms to discuss Hawking effect, is put forwarded. An interesting advantage of this reformulated HJ method is that one can get directly the emission spectrum from the event horizon of the black hole, which was missing in the earlier literature. Also, the quantization of the entropy and area of a black hole is discussed in this method. Another part of the thesis is the introduction of a new type of global embedding of curved space-time to higher dimensional Minkowskian space-time (GEMS). Using this a unified description of the Hawking and Unruh effects is given. Advantage of this approach is, it simplifies as well as generalises the conventional embedding. In addition to the spherically symmetric space-times, the Kerr-Newman black hole is exemplified. Finally, following the above ideas and the definition of partition function for gravity, it is shown that extremization of entropy leads to the Einstein's equations of motion. In this frame work, a relation between the entropy, energy and the temperature of a black hole is given where energy is shown to be the Komar expression. Interestingly, this relation is the generalized Smarr formula. In this analysis, the GEMS method provides the law of equipartition of energy as an intermediate step.

Ph.D. thesis (arXiv version). 139 pages, including the front matter. Supervisor: Rabin Banerjee. Institution: S.N. Bose National Centre for Basic Sciences, Kolkata, India. Degree awarded on 23 August 2011 from University of Calcutta, Kolkata, India

References in corpus (1)

• Hawking Radiation and Entropy from Horizon Degrees of Freedom

Cited by in corpus (10)

• Near horizon local instability and quantum thermality
• Temperature and thermodynamic structure of Einstein's equations for a cosmological black hole
• Detector response along null geodesics in black hole spacetimes and in a Friedmann-Lemaitre-Robertson-Walker Universe
• Local free-fall Temperature of GMGHS Black Holes
• Near horizon hidden symmetry and entropy of Sultana-Dyer black hole: A time dependent case
• Hawking radiation in a non-covariant frame: the Jacobi metric approach
• Horizon thermalization of Kerr black hole through local instability
• Conformal Vacuum and Fluctuation-Dissipation in de-Sitter Universe and Black Hole Spacetimes
• Local free-fall Temperature of modified Schwarzschild black hole in rainbow spacetime
• Thermal nature of a generic null surface