Relic Radiation from an Evaporating Black Hole

Abstract

We present a non-string-theoretic calculation of the microcanonical entropy of relic integer-spin Hawking radiation -- at fixed total energy $E$. The only conserved macroscopic quantity is the total energy $E$ (the total energy of the relic radiation). Data for a boundary-value approach, with massless, integer-spin perturbations, are set on initial and final space-like hypersurfaces. In the resulting 1-dimensional statistical-mechanics problem, the real part of the (complex) time separation at spatial infinity, $T=\mid T\mid \exp (-i\delta ),\delta >0$, is the variable conjugate to the total energy. We count the number of weak-field configurations on the final space-like hypersurface with energy $E$. One recovers the Cardy formula and the Bekenstein-Hawking entropy, if Re(T) is of the order of the black-hole life- time, leading to a statistical interpretation of black-hole entropy. The microcanonical entropy includes a logarithmic correction to the black-hole area law, which is {\it universal} (independent of black-hole parameters). Here, the discreteness of the energy levels is crucial. This approach is compared with that of string theory for the transition to the fundamental-string régime in the final stages of evaporation. The squared coupling, $g^2$, regulating the transition to a highly-excited string state and {\it vice versa}, can be related to the angle, $\delta$, of complex-time rotation above. The strong-coupling régime corresponds to a Euclidean black hole, while the physical limit of a Lorentzian space-time (as $\delta \to 0_{+}$) corresponds to the weak-coupling régime. This resembles the transition to a highly-excited string-like state which subsequently decays into massless particles, thereby avoiding the naked singularity.

To appear in International Journal of Modern Physics D

References in corpus (37)

• Logarithmic correction to the Bekenstein-Hawking entropy
• Black Hole Entropy from Loop Quantum Gravity
• A Correspondence Principle for Black Holes and Strings
• Logarithmic Corrections to Black Hole Entropy from the Cardy Formula
• String Theory and the Principle of Black Hole Complementarity
• Self Gravitating Fundamental Strings
• Strings, Black Holes and Lorentz Contraction
• Self-gravitating fundamental strings and black-holes
• Entropy of Schwarzschild black hole and string-black hole correspondence
• String Balls at the LHC and Beyond
• Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula
• An Uncertainty Relation of Space-Time
• Statistical Mechanics of Black Holes
• Vaidya Space-Time in Black-Hole Evaporation
• Schwarzschild black hole as a grand canonical ensemble
• Self-Gravitating Strings and String/Black Hole Correspondence
• Quantum Mechanics of a Black Hole
• Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy
• A Stringy Correspondence Principle in Cosmology
• Conceptual unification of elementary particles, black holes, quantum de Sitter and Anti de Sitter string states
• Anti-de Sitter black holes, perfect fluids, and holography
• A Phase Space Approach to the Gravitational Arrow of Time
• Scalar--Field Amplitudes in Black--Hole Evaporation
• Black Holes, Interactions, and Strings
• UHECR as Decay Products of Heavy Relics? The Lifetime Problem
• The Size of a Polymer of String-Bits: A Numerical Investigation
• Coherent and squeezed states in black-hole evaporation
• A Phase Space Approach to Gravitational Enropy
• Black Hole Entropy from a Highly Excited Elementary String
• Entropy and String Black Hole Correspondence
• Black Holes and Strings: the Polymer Link
• High Energy Effects on D-Brane and Black Hole Emission Rates
• Quantum amplitudes in black-hole evaporation: Spins 1 and 2
• Asymptotic Density of Open p-brane States with Zero-modes included
• Effectiveness of One-dimensional gas models for black holes
• Black Holes, Space-Filling Chains and Random Walks
• Remarks on Black Hole Degrees of Freedom in String Theory

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