Wheeler DeWitt states of a charged AdS4 black hole

Acknowledgements: We are especially grateful to Sean Hartnoll for extensive feedback on an early draft of this paper. It is also a pleasure to thank Joseph Conlon, Fernando Quevedo, Ronak M Soni, Aron Wall and Zhenbin Yang for useful conversations. S.N. would like to thank DAMTP at the University of Cambridge and the University of Southampton for their hospitality while the majority of this work was being done. Finally, S.N. would like to specially thank Pam Kivelson and Steven Kivelson for their kind suggestions and warm encouragement. M.J.B. was supported by a Gates Cambridge Scholarship (#OPP1144). S.N. was supported by the China Scholarship Council-FaZheng Group at the University of Oxford.Abstract We solve the Wheeler DeWitt equation for the planar Reissner-Nordström-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 gxx 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.