Thermal Hawking Broadening and Statistical Entropy of Black Hole Wave Packet

TL;DR

This paper investigates the quantum structure of Schwarzschild black holes using a minimal uncertainty wave packet, revealing thermal broadening effects and deriving the entropy, including quantum corrections, in a semi-classical framework.

Contribution

It introduces a non-singular Hartle-Hawking wave packet approach to analyze black hole microstates and derives the statistical entropy with quantum corrections.

Findings

Exact Bekenstein-Hawking entropy recovered semi-classically

Thermal Hawking broadening linked to Compton width of microstates

Minimal entropy black wave packet with Planck-scale tail

Abstract

The quantum mechanical structure of Schwarzschild black hole is probed, in the mini super spacetime, by means of a non-singular minimal uncertainty Hartle-Hawking wave packet. The Compton width of the microstate probability distribution is translated into a thermal Hawking broadening of the mass spectrum. The statistical entropy is analytically calculated using the Fowler prescription. While the exact Bekenstein-Hawking entropy is recovered at the semi classical limit, the accompanying logarithmic tail gives rise to a Planck size minimal entropy black wave packet.