Thermal Hawking Broadening and Statistical Entropy of Black Hole Wave Packet

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.