Wheeler DeWitt States of a Charged AdS$_4$ Black Hole

TL;DR

This paper solves the Wheeler DeWitt equation for a charged AdS4 black hole, constructing semiclassical states that connect black hole interior solutions to boundary dual theories, revealing insights into quantum fluctuations and thermodynamics.

Contribution

It provides a novel construction of Wheeler DeWitt states for charged AdS black holes and explores their evolution through horizons and relation to boundary thermodynamics.

Findings

Quantum fluctuations dominate near the singularity.

States recover the Lorentzian partition function of the dual theory.

Wheeler DeWitt states encode black hole thermodynamics.

Abstract

We solve the Wheeler DeWitt equation for the planar Reissner-Nordstr\"om-AdS black hole in a minisuperspace approximation. We construct semiclassical Wheeler DeWitt states from Gaussian wavepackets that are peaked on classical black hole interior solutions. By using the metric component $g_{xx}$ as a clock, these states are evolved through both the exterior and interior horizons. Close to the singularity, we show that quantum fluctuations in the wavepacket become important, and therefore the classicality of the minisuperspace approximation breaks down. Towards the AdS boundary, the Wheeler DeWitt states are used to recover the Lorentzian partition function of the dual theory living on this boundary. This partition function is specified by an energy and a charge. Finally, we show that the Wheeler DeWitt states know about the black hole thermodynamics, recovering the grand canonical thermodynamic potential after an appropriate averaging at the black hole horizon.