Quantum Black Hole Wave Packet: Average Area Entropy and Temperature Dependent Width

Abstract

A quantum Schwarzschild black hole is described, at the mini super spacetime level, by a non-singular wave packet composed of plane wave eigenstates of the momentum Dirac-conjugate to the mass operator. The entropy of the mass spectrum acquires then independent contributions from the average mass and the width. Hence, Bekenstein's area entropy is formulated using the $⟨{\text{mass}}^2⟩$ average, leaving the $⟨\text{mass}⟩$ average to set the Hawking temperature. The width function peaks at the Planck scale for an elementary (zero entropy, zero free energy) micro black hole of finite rms size, and decreases Doppler-like towards the classical limit.

5 PRD pages, 1 figure; v.2 minor typo corrections

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• Horizon of quantum black holes in various dimensions
• Horizons and non-local time evolution of quantum mechanical systems
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• Quantum torsion and a Hartle-Hawking "beam''
• A new length scale, and modified Einstein-Cartan-Dirac equations for a point mass
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