Schwarzschild Mass Uncertainty

TL;DR

This paper develops a quantum mechanical framework for Schwarzschild black holes, deriving a Hamiltonian resembling an upside down harmonic oscillator, leading to quantized horizon areas and a universal uncertainty structure.

Contribution

It introduces a novel quantum approach to Schwarzschild black holes using Dirac's constrained systems, resulting in a quantized horizon area and a universal uncertainty principle.

Findings

Average horizon surface area is linearly quantized.

Wave packets form an orthonormal, non-singular tower with equally spaced energy levels.

Universal quantum uncertainty affects the Schwarzschild sector at all mass scales.

Abstract

Applying Dirac's procedure to $r$-dependent constrained systems, we derive a reduced total Hamiltonian, resembling an upside down harmonic oscillator, which generates the Schwarzschild solution in the mini super-spacetime. Associated with the now $r$-dependent Schrodinger equation is a tower of localized Guth-Pi-Barton wave packets, orthonormal and non-singular, admitting equally spaced average-'energy' levels. Our approach is characterized by a universal quantum mechanical uncertainty structure which enters the game already at the flat spacetime level, and accompanies the massive Schwarzschild sector for any arbitrary mean mass. The average black hole horizon surface area is linearly quantized.