Semiclassical gravitational collapse of a radially symmetric massless scalar quantum field

Abstract

We present a method to study the semiclassical gravitational collapse of a radially symmetric scalar quantum field in a coherent initial state. The formalism utilizes a Fock space basis in the initial metric, is unitary and time reversal invariant up to numerical precision. It maintains exact compatibility of the metric with the expectation values of the energy momentum tensor in the scalar field coherent state throughout the entire time evolution. We find a simple criterion for the smallness of discretization effects, which is violated when a horizon forms. As a first example, we study the collapse of a specific state in the angular momentum $l=0$ approximation. Outside the simulated volume it produces a Schwarzschild metric with $r_s\sim 3.5{\ell }_p$. We see behaviour that is compatible with the onset of horizon formation both in the semiclassical and corresponding classical cases in a regime where we see no evidence for large discretization artefacts. In our example setting, we see that quantum effects accelerate the possible horizon formation and move it radially outward. We find that this effect is robust against variations of the radial resolution, the time step, the volume, the initial position and shape of the inmoving state, the vacuum subtraction, the discretization of the time evolution operator and the integration scheme of the metric. We briefly discuss potential improvements of the method and the possibility of applying it to black hole evaporation. We also briefly touch on the extension of our formalism to higher angular momenta, but leave the details and numerics for a forthcoming publication.

arXiv commentv2: 54 pages, 32 figures. Version to appear in PRD

References in corpus (16)

• Thermodynamics of Spacetime: The Einstein Equation of State
• Black Holes: Complementarity or Firewalls?
• Evanescent Black Holes
• The information paradox: A pedagogical introduction
• Critical phenomena in gravitational collapse
• Black hole unitarity and antipodal entanglement
• News from Critical Collapse: Bondi Mass, Tails and Quasinormal Modes
• Self-Similar Collapse of Scalar Field in Higher Dimensions
• Critical Behavior of Black Hole Formation in a Scalar Wave Collapse
• Black Hole as a Quantum Field Configuration
• Classical-Quantum Correspondence and Hawking Radiation
• Gravitational collapse of quantum fields and Choptuik scaling
• Gravitational collapse with quantum fields
• Wave Functions for Quantum Black Hole Formation in Scalar Field Collapse
• Gravitational Collapse and Calogero Model
• Black Hole Decay and Quantum Instantons

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