Annihilation-to-nothing: a quantum gravitational boundary condition for the Schwarzschild black hole

Abstract

The interior of a static Schwarzschild metric can be written in terms of two functions, similar to some models of anisotropic cosmology. With a suitable choice of canonical variables, we solve the Wheeler-DeWitt equation (WDW) inside the horizon of a Schwarzschild black hole. By imposing classicality near the horizon, and requiring boundedness of the wave function, we get a rather generic solution of the WDW equation, whose steepest-descent solution, i.e., the ridge of the wave function, coincides nicely with the classical trajectory. However, there is an ambiguity in defining the arrow of time which leads to two possible interpretations - (i) if there is only one arrow of time, one can infer that the steepest-descent of the wave function follows the classical trajectory throughout: coming from the event horizon and going all the way down to the singularity, while (ii) if there are two different arrows of time in two separate regimes, it can be inferred that the steepest-descent of the wave function comes inwards from the event horizon in one region while it moves outwards from the singularity in the other region, and there exists an annihilation process of these two parts of the wave function inside the horizon. Adopting the second interpretation could shed light on the information loss paradox: as time goes on, probabilities for histories that include black holes and singularities decay to zero and eventually only trivial geometries dominate.

arXiv comment20 pages, 7 figures

References in corpus (51)

• Eternal Black Holes in AdS
• Black Holes: Complementarity or Firewalls?
• Formation and evaporation of non-singular black holes
• Noncommutative geometry inspired Schwarzschild black hole
• New Regular Black Hole Solution from Nonlinear Electrodynamics
• Information Loss in Black Holes
• An Apologia for Firewalls
• Black hole evaporation: A paradigm
• Black Hole Remnants and the Information Loss Paradox
• Quantum Transfiguration of Kruskal Black Holes
• Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling
• Loop quantum black hole
• The Classical Universes of the No-Boundary Quantum State
• Noncommutative Quantum Cosmology
• The No-Boundary Measure of the Universe
• Effective line elements and black-hole models in canonical (loop) quantum gravity
• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• The Wave Function of Vasiliev's Universe - A Few Slices Thereof
• Covariance in models of loop quantum gravity: Spherical symmetry
• Polymer Schwarzschild black hole: An effective metric
• Towards Noncommutative Quantum Black Holes
• Quantum gravity predictions for black hole interior geometry
• The causal structure of dynamical charged black holes
• Is the firewall consistent?: Gedanken experiments on black hole complementarity and firewall proposal
• Hamiltonian Formalism for Black Holes and Quantization
• Some implications of signature-change in cosmological models of loop quantum gravity
• Constructing a counterexample to the black hole complementarity
• Semi-classical black holes with large N re-scaling and information loss problem
• Naked Black Hole Firewalls
• Asymptotic non-flatness of an effective black hole model based on loop quantum gravity
• Spherically symmetric canonical quantum gravity
• Black hole complementarity and firewall in two dimensions
• Thin-shell bubbles and information loss problem in anti de Sitter background
• Signature change in 2-dimensional black-hole models of loop quantum gravity
• Information loss, made worse by quantum gravity?
• Loops rescue the no-boundary proposal
• Two dimensional Nearly de Sitter gravity
• Thermal activation of thin-shells in anti-de Sitter black hole spacetime
• Complementary Test of the Dark Matter Self-Interaction by Direct and Indirect Detections
• Effective black-to-white hole bounces: The cost of surgery
• Quantum Transitions Between Classical Histories: Bouncing Cosmologies
• Fuzzy Euclidean wormholes in de Sitter space
• Dynamics of magnetic shells and information loss problem
• Status report: black hole complementarity controversy
• Hawking radiation as instantons
• Comment (2) on "Quantum Transfiguration of Kruskal Black Holes"
• Two Wave Functions and dS/CFT on S^1 x S^2
• The no-boundary wave function for loop quantum cosmology
• Non-bouncing solutions in loop quantum cosmology
• Can a false vacuum bubble remove the singularity inside a black hole?
• Properties of fluctuating states in loop quantum cosmology

Cited by in corpus (16)

• Wheeler-DeWitt states of the AdS-Schwarzschild interior
• Annihilation-to-nothing: DeWitt boundary condition inside a black hole
• Black hole singularity resolution in unimodular gravity from unitarity
• On Black Hole Thermodynamics, Singularity, and Gravitational Entropy
• Wheeler-DeWitt equation beyond the cosmological horizon: Annihilation to nothing, infinity avoidance, and loss of quantum coherence
• Spinorial Wheeler-DeWitt wave functions inside black hole horizons
• Before the Page time: maximum entanglements or the return of the monster?
• Trouble with geodesics in black-to-white hole bouncing scenarios
• Early Dark Energy During Big Bang Nucleosynthesis
• Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario
• Quantum Schwarzschild-(A)dS Black Holes: Unitarity and Singularity Resolution
• Future Boundaries and the Black Hole Information Paradox
• Hybrid inflation and gravitational waves from accidentally light scalars
• Singularity avoidance from path integral
• Two faces of Hawking radiation and thin-shell emission: pair-creation vs. tunneling
• Black-hole models in loop quantum gravity