Adiabatic Invariant Treatment of a Collapsing Sphere of Quantized Dust

TL;DR

This paper investigates the quantum collapse of a dust sphere using adiabatic invariants, revealing how quantum effects and particle creation influence the collapse dynamics.

Contribution

It introduces an adiabatic invariant approach to analyze quantum dust collapse, providing new insights into non-adiabatic corrections and back-reaction effects.

Findings

Quantum corrections slow down collapse.

Particle creation impacts collapse dynamics.

Back-reaction effects are quantitatively estimated.

Abstract

The semiclassical collapse of a sphere of quantized dust is studied. A Born-Oppenheimer decomposition is performed for the wave function of the system and the semiclassical limit is considered for the gravitational part. The method of adiabatic invariants for time dependent Hamiltonians is then employed to find (approximate) solutions to the quantum dust equations of motions. This allows us to obtain corrections to the adiabatic approximation of the dust states associated with the time evolution of the metric. The diverse non-adiabatic corrections are generally associated with particle (dust) creation and related fluctuations. The back-reaction due to the dominant contribution to particle creation is estimated and seen to slow-down the collapse.