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Wheeler-DeWitt states of the AdS-Schwarzschild interior

Sean A. Hartnoll
Aug 2022
摘要
We solve the Wheeler-DeWitt equation for the planar AdS-Schwarzschildinterior in a minisuperspace approximation involving the volume and spatialanisotropy of the interior. A Gaussian wavepacket is constructed that is peakedon the classical interior solution. Simple observables are computed using thiswavepacket, demonstrating the freedom to a choose a relational notion of`clock' in the interior and characterizing the approach to the spacelikesingularity. The Wheeler-DeWitt equation may be extended out through thehorizon, where it describes the holographic renormalization group flow of theblack hole exterior. This amounts to the Hamilton-Jacobi evolution of themetric component $g_{tt}$ from positive interior values to negative exteriorvalues. The interior Gaussian wavepacket is shown to evolve into the Lorentizanpartition function of the boundary conformal field theory over a microcanonicalenergy window.
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