Gravitational collapse of a shell of quantized matter

The semiclassical collapse, including lowest-order back-reaction, of a thin shell of self-gravitating quantized matter is illustrated. The conditions for which self-gravitating matter forms a thin shell are first discussed and an effective Lagrangian for such matter is obtained. The matter-gravity system is then quantized, the semiclassical limit for gravitation is taken and the method of adiabatic invariants is applied to the resulting time-dependent matter Hamiltonian. The governing equations are integrated numerically, for suitable initial conditions, in order to illustrate the effect of back-reaction, due to the creation of matter, in slowing down the collapse near the horizon.