Adiabatic Invariant Treatment of a Collapsing Sphere of Quantized Dust

Details Adiabatic Invariant Treatment of a Collapsing Sphere of Quantized Dust Adiabatic Invariant Treatment of a Collapsing Sphere of Quantized Dust

1997-06-24

arxiv.org/abs/gr-qc/9706074v2

Class.Quant.Grav. 15 (1998) 2451-2464

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 16 pages, no figures, final version to appear in Class. and Quantum Gravity

Scientific paper

10.1088/0264-9381/15/8/021

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.

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