Adiabatic Invariant Treatment of a Collapsing Sphere of Quantized Matter

The semiclassical collapse of a sphere of quantized scalar matter is studied. A BornOppenheimer 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 scalar field equations of motions. This allows us to obtain corrections to the adiabatic approximation of the matter states associated with the time evolution of the metric. The diverse non-adiabatic corrections are generally associated with particle creation and related fluctuations. The back-reaction due to the dominant contribution to particle creation is estimated and seen to slow-down the collapse. e–mail: [email protected] e–mail: [email protected] e–mail: [email protected] 0