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

TL;DR

This paper models a quantum Schwarzschild black hole as a non-singular wave packet, linking its entropy to average mass and width, and explores how these properties relate to temperature and the classical limit.

Contribution

It introduces a wave packet description of quantum black holes that incorporates width-dependent entropy and temperature, connecting quantum properties to classical black hole thermodynamics.

Findings

Width peaks at the Planck scale for micro black holes.

Entropy depends on the average squared mass, not just the mean.

Width decreases towards the classical limit, resembling a Doppler effect.

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 $\langle \text{mass}^2 \rangle$ average, leaving the $\langle \text{mass} \rangle$ 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.