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Wave functions for the Schwarschild black hole interior

Daniel Cartin·Gaurav Khanna
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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 $γ$ to the quantum ambiguity $δ$ appearing in the model. This bound is violated when we use a natural value for $δ$ based on loop quantum gravity together with a recent proposal for $γ$. We also present numerical solutions of the constraint.

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Daniel Cartin, Gaurav Khanna. 2006-04-08. Wave functions for the Schwarschild black hole interior. https://doi.org/10.1103/physrevd.73.104009

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