Schrodinger formalism, black hole horizons and singularity behavior

Abstract

The Gauss-Codazzi method is used to discuss the gravitational collapse of a charged Reisner-Nordström domain wall. We solve the classical equations of motion of a thin charged shell moving under the influence of its own gravitational field and show that a form of cosmic censorship applies. If the charge of the collapsing shell is greater than its mass, then the collapse does not form a black hole. Instead, after reaching some minimal radius, the shell bounces back. The Schrodinger canonical formalism is used to quantize the motion of the charged shell. The limits near the horizon and near the singularity are explored. Near the horizon, the Schrodinger equation describing evolution of the collapsing shell takes the form of the massive wave equation with a position dependent mass. The outgoing and incoming modes of the solution are related by the Bogolubov transformation which precisely gives the Hawking temperature. Near the classical singularity, the Schrodinger equation becomes non-local, but the wave function describing the system is non-singular. This indicates that while quantum effects may be able to remove the classical singularity, it may also introduce some new effects.

10 pages; v2 added references and further comment on singularity behavior, version to appear in PRD

References in corpus (8)

• Regular black holes and black universes
• Observation of Incipient Black Holes and the Information Loss Problem
• Open String Creation by S-Branes
• Quantum Radiation from Quantum Gravitational Collapse
• Hawking radiation as seen by an infalling observer
• Quantum gravitational collapse: non-singularity and non-locality
• Constructing a counterexample to the black hole complementarity
• Collapsing and static thin massive charged dust shells in a Reissner-Nordström black hole background in higher dimensions

Cited by in corpus (35)

• Singularities and the Finale of Black Hole Evaporation
• Radiation from a collapsing object is manifestly unitary
• Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity
• Non-local (but also non-singular) physics at the last stages of gravitational collapse
• Quantitative approaches to information recovery from black holes
• Horizon Quantum Mechanics: a hitchhiker's guide to quantum black holes
• Schrödinger and Klein-Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse
• Time dependent fluctuations and particle production in cosmological de Sitter and anti-de Sitter spaces
• Polymer Quantization of a Self-Gravitating Thin Shell
• Non-perturbative correction to the Horava-Lifshitz black hole thermodynamics
• A regular black hole as the final state of evolution of a singular black hole
• Resolving the Schwarzschild singularity in both classic and quantum gravity
• Spontaneous Radiation of Black Holes
• Quantum oscillations in the black hole horizon
• A squeeze-like operator approach to position-dependent mass in quantum mechanics
• Quantum space and quantum completeness
• Unitarity in Reissner-Nordström background: striding away from information loss
• Hawking-like radiation and the density matrix for an infalling observer during gravitational collapse
• Information Missing Puzzle, Where Is Hawking's Error?
• Coordinate representation of particle dynamics in AdS and in generic static spacetimes
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Quantum Collapse of a Thin Shell Revisited
• Exact Inner Metric and Microscopic State of AdS${}_3$-Schwarzschld BHs
• Information loss paradox revisited: farewell firewall?
• Time Evolution of Temperature and Entropy of Various Collapsing Domain Walls
• Quantum Collapse of a Charged $n$-dimensional BTZ-like Domain Wall
• Classical and Quantum Equations of Motion of an n-dimesional BTZ Black Hole
• Proper time Quantization of a Thin Shell
• Massive scalar wave packet emission by a charged Black Hole and Cosmic Censorship Conjecture violation
• Gravity Induced Spontaneous Radiation
• An analytic model for a total process of gravitational collapse: From star to Schwarzschild black hole
• Time as a test-field: the no-boundary universe in motion and a smooth radiation bounce
• Volume Renormalization and the Higgs
• Correction to Hawking radiation in non-singular gravitational collapse
• Directional Quantum Singularities in Curzon Spacetime