Complete Semiclassical Treatment of the Quantum Black Hole Problem (original) (raw)
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Developments in black hole research: Classical, semi-classical, and quantum
Arxiv preprint arXiv:0711.2279, 2007
The possible existence of black holes has fascinated scientists at least since Michell and Laplace's proposal that a gravitating object could exist from which light could not escape. In the 20th century, in light of the general theory of relativity, it became apparent that, were such objects to exist, their structure would be far richer than originally imagined. Today, astronomical observations strongly suggest that either black holes, or objects with similar properties, not only exist but may well be abundant in our universe. In light of this, black hole research is now not only motivated by the fascinating theoretical properties such objects must possess but also as an attempt to better understand the universe around us. We review here some selected developments in black hole research, from a review of its early history to current topics in black hole physics research. Black holes have been studied at all levels; classically, semi-classically, and more recently, as an arena to test predictions of candidate theories of quantum gravity. We will review here progress and current research at all these levels as well as discuss some proposed alternatives to black holes.
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Quantum Mechanical Black Holes: Towards a Unification of Quantum Mechanics and General Relativity
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Lecture Notes in Physics, 2012
CONTENTS ifcation of Type-II string on K 3 × T 2. This leads to a four-dimensional theory with N = 4 supersymmetry and 22 vector multiplets. Our objective will be to understand the entropy of half-BPS and quarter-BPS black holes in this theory both from the thermodynamic and statistical view points. A lot is known about generalization of these results to other compactifications. For a review of these generalization and of some of the material covered here see [1, 2]. There has also been more progress both in defining the quantum entropy using AdS/CF T correspondence and in computing it using localization. For a review see [3]. We will not discuss these more recent topics here to keep the discussion simple and more accessible. The organization is as follows. We review aspects of classical and semiclassical black holes in chapters §1 and §2, and elements of string theory in chapter §3. The microscopic counting is then described in chapters §4 and §5 and the comparison with macroscopic entropy is discussed in §6. Relevant mathematical background is covered in §7. These lecture notes are aimed at beginning graduate students but assume some basic background in General Theory of Relativity, Quantum Field Theory, and String Theory. A good introductory textbook on general relativity from a modern perspective see [4]. For a more detailed treatment see [5] which has become a standard reference among relativists, and [6] which remains a classic for various aspects of general relativity. For quantum field theory in curved spacetime see [7]. For relevant aspects of string theory see [8, 9, 10, 11].