Semiclassical gravitational collapse of a radially symmetric massless scalar quantum field

Jana N. Guenther (1) , Christian Hoelbling , Lukas Varnhorst (1)

1 CPT - Centre de Physique Théorique - UMR 7332

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 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

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Réseau [hep-lat]; Physique des Hautes Energies - Théorie [hep-th]

Jana N. Guenther, Christian Hoelbling, Lukas Varnhorst. Semiclassical gravitational collapse of a radially symmetric massless scalar quantum field. Physical Review D, 2022, 105 (10), pp.105010. ⟨10.1103/PhysRevD.105.105010⟩. ⟨hal-02999586⟩