Semiclassical gravitational collapse of a radially symmetric massless scalar quantum field
Résumé
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 approximation. Outside the simulated volume, it produces a Schwarzschild metric with . We see behavior 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 artifacts. 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.
Mots clés
gravitation: semiclassical
gravitation: collapse
horizon: formation
effect: discrete
time: discrete
field theory: scalar: massless
field theory
metric: Schwarzschild
effect: quantum
time reversal: invariance
tensor: energy-momentum
black hole: evaporation
coherent state
initial state
resolution
Fock space
unitarity
coherence
boundary condition