Schwarzschild mass uncertainty

Aharon Davidson, Ben Yellin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish
Article number1662
Pages (from-to)1-11
Number of pages11
JournalGeneral Relativity and Gravitation
Volume46
Issue number2
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Black hole
  • Constrained system
  • Mini super spacetime
  • Schrodinger equation
  • Wave packet

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