Wave functions for the Schwarschild black hole interior

Abstract

Using the Hamiltonian constraint derived by Ashtekar and Bojowald, we look for pre-classical wave functions in the Schwarzschild interior. In particular, when solving this difference equation by separation of variables, an inequality is obtained relating the Immirzi parameter $\gamma$ to the quantum ambiguity $\delta$ appearing in the model. This bound is violated when we use a natural value for $\delta$ based on loop quantum gravity together with a recent proposal for $\gamma$. We also present numerical solutions of the constraint.

15 pages, 4 figures, published version

References in corpus (2)

• Black hole evaporation: A paradigm
• The Bianchi IX model in Loop Quantum Cosmology

Cited by in corpus (6)

• Loop Quantum Dynamics of the Schwarzschild Interior
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Lattice refining loop quantum cosmology, anisotropic models and stability
• Fermions in Loop Quantum Cosmology and the Role of Parity
• Instabilities in numerical loop quantum cosmology
• Quantum Geometry and its Implications for Black Holes