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.

arXiv comment31 pages. 1 figure. v2 minor improvements. v3 minor improvements

References in corpus (35)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• A Stress Tensor for Anti-de Sitter Gravity
• Eternal Black Holes in AdS
• Black holes and the butterfly effect
• Lecture Notes on Holographic Renormalization
• Cool horizons for entangled black holes
• Complexity Equals Action
• Complexity and Shock Wave Geometries
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Surface Terms as Counterterms in the AdS/CFT Correspondence
• On the Holographic Renormalization Group
• Complexity, action, and black holes
• Holographic and Wilsonian Renormalization Groups
• String Cosmology: A Review
• The Black Hole Singularity in AdS/CFT
• The Quantum Gravity Dynamics of Near Extremal Black Holes
• Holography at finite cutoff with a $T^2$ deformation
• The Wave Function of Vasiliev's Universe - A Few Slices Thereof
• Complexity and the bulk volume, a new York time story
• Diving into a holographic superconductor
• The boundary dual of the bulk symplectic form
• Gravitational duals to the grand canonical ensemble abhor Cauchy horizons
• Proper time to the black hole singularity from thermal one-point functions
• Inflationary Consistency Conditions from a Wavefunctional Perspective
• Holographic flows from CFT to the Kasner universe
• Bath deformations, islands and holographic complexity
• Page Curves and Bath Deformations
• Gravitational path integral from the $T^2$ deformation
• Trans-IR Flows to Black Hole Singularities
• Annihilation-to-nothing: a quantum gravitational boundary condition for the Schwarzschild black hole
• RG Flows and Thermofield-Double States in Holography
• Speculation about the black hole final state: resolving singularity by quantum gravity
• What's inside a hairy black hole in massive gravity?
• Kasner geometries inside holographic superconductors
• Space-like Singularities of General Relativity: A Phantom menace?

Cited by in corpus (13)

• Black hole interiors in holographic topological semimetals
• Kasner interiors from analytic hairy black holes
• AdS Black Holes with a Bouncing Interior
• Shock waves, black hole interiors and holographic RG flows
• Black hole singularity resolution in unimodular gravity from unitarity
• Mixmasters in Wonderland: Chaotic dynamics from Carroll limits of gravity
• Diving inside holographic metals
• Spinorial Wheeler-DeWitt wave functions inside black hole horizons
• Quantum Schwarzschild-(A)dS Black Holes: Unitarity and Singularity Resolution
• Cyclic Kruskal Universe: a quantum-corrected Schwarzschild black hole in unitary unimodular gravity
• Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity
• Radial canonical $\Lambda <0$ gravity
• York time in JT gravity