Wheeler-DeWitt states of the AdS-Schwarzschild interior

Abstract

We solve the Wheeler-DeWitt equation for the planar AdS-Schwarzschild interior in a minisuperspace approximation involving the volume and spatial anisotropy of the interior. A Gaussian wavepacket is constructed that is peaked on the classical interior solution. Simple observables are computed using this wavepacket, demonstrating the freedom to a choose a relational notion of `clock' in the interior and characterizing the approach to the spacelike singularity. The Wheeler-DeWitt equation may be extended out through the horizon, where it describes the holographic renormalization group flow of the black hole exterior. This amounts to the Hamilton-Jacobi evolution of the metric component $g_{tt}$ from positive interior values to negative exterior values. The interior Gaussian wavepacket is shown to evolve into the Lorentizan partition function of the boundary conformal field theory over a microcanonical energy window.