The Volume Operator in Spherically Symmetric Quantum Geometry

Abstract

The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger spherically symmetric volume spectrum adds fine structure to the homogeneous spectrum. The formulas of this paper complete the derivation of an explicit calculus for spherically symmetric models which is needed for future physical investigations.

25 pages, 2 figures

References in corpus (3)

• Spherically Symmetric Quantum Geometry: States and Basic Operators
• The Bianchi IX model in Loop Quantum Cosmology
• Qualitative Approach to Semi-Classical Loop Quantum Cosmology

Cited by in corpus (5)

• Black hole evaporation: A paradigm
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Degenerate Configurations, Singularities and the Non-Abelian Nature of Loop Quantum Gravity
• The Early Universe in Loop Quantum Cosmology
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity