Quantum Mechanics of a Black Hole

Abstract

Beginning with Bekenstein, many authors have considered a uniformly spaced discrete quantum spectrum for black hole horizon area. It is also believed that the huge degeneracy of these area levels corresponds to the notion of black hole entropy. Starting from these two assumptions we here infer the algebra of a Schwarzschild black hole's observables. This algebra then serves as motivation for introducing in the system's Hamiltonian an interaction term. The interaction contains the horizon area operator, which is a number operator, and its canonical conjugate, the phase operator. The Hawking radiation from a Schwarzschild black hole is seen to be a consequence of an area-phase interaction. Using this interaction we have reproduced the semi-classical result for the Hawking radiation power. Furthermore, we show that the initial state of the black hole determines the nature of its development. Thus, a state which is an area eigenstate describes a static eternal black hole, but a coherent state describes a radiating black hole. Hence, it is the observer's initial knowledge or uncertainty about the horizon area which determines the evolution.

RevTex, 30 pages, Accepted for publication in Physical Review D

References in corpus (3)

• Best Approximation to a Reversible Process in Black-Hole Physics and the Area Spectrum of Spherical Black Holes
• Fluctuations of the Hawking Flux
• Schwarzschild black hole as a grand canonical ensemble

Cited by in corpus (13)

• Gravity and the Thermodynamics of Horizons
• Entropy of Static Spacetimes and Microscopic Density of States
• Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections
• The Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
• Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy
• Building blocks of a black hole
• Schwarzschild black hole as a grand canonical ensemble
• Quantum Mechanical Spectra of Charged Black Holes
• Holographic Shell Model: Stack Data Structure inside Black Holes
• Black Hole Thermodynamics without a Black Hole?
• Critical Exponents For Schwarzschild-Kerr and BTZ Systems
• Relic Radiation from an Evaporating Black Hole
• Spectroscopy of an AdS Reissner-Nordstrom black hole