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

Abstract

A quantum Schwarzschild black hole will be described at the mini super space time 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. Bekenstein-Hawking area entropy is formulated using the mass2 average, leaving the 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.