Adiabatic invariant treatment of a collapsing sphere of quantized dust

The semiclassical collapse of a sphere of quantized dust is studied. A Born-Oppenheimer decomposition is performed for the wavefunction 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 motion. 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