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 an d an effective Lagrangian for such matter is obtained. The matter-gravity s ystem is then quantized, the semiclassical limit for gravitation is taken a nd the method of adiabatic invariants is applied to the resulting time-depe ndent matter Hamiltonian. The governing equations are integrated numericall y, for suitable initial conditions, in order to illustrate the effect of ba ck-reaction, due to the creation of matter, in slowing down the collapse ne ar the horizon.