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

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Cited by in corpus (27)

• Quantum Transfiguration of Kruskal Black Holes
• Quantum Extension of the Kruskal Space-time
• Loop Quantum Dynamics of the Schwarzschild Interior
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Lattice refining loop quantum cosmology, anisotropic models and stability
• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• Properties of a recent quantum extension of the Kruskal geometry
• Numerical loop quantum cosmology: an overview
• Von-Neumann Stability and Singularity Resolution in Loop Quantized Schwarzschild Black Hole
• How Information Crosses Schwarzschild's Central Singularity
• Fermions in Loop Quantum Cosmology and the Role of Parity
• Numerical Techniques in Loop Quantum Cosmology
• Hamiltonian formulation and loop quantization of a recent extension of the Kruskal spacetime
• Instabilities in numerical loop quantum cosmology
• Von Neumann stability of modified loop quantum cosmologies
• Exploring alternatives to the Hamiltonian calculation of the Ashtekar-Olmedo-Singh black hole solution
• Quantum Geometry and its Implications for Black Holes
• Extended phase space quantization of a black hole interior model in Loop Quantum Cosmology
• Geodetic precession and shadow of quantum extended black holes
• Axial perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology
• Decoding quantum gravity information with black hole accretion disk
• Symmetric black-to-white hole solutions with a cosmological constant
• Polar perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology
• Quantum geometry and black holes
• Quantum Black Hole as a Harmonic Oscillator from the Perspective of the Minimum Uncertainty Approach
• Singularity avoidance from path integral