Gravitational Collapse of a Shell of Quantized Matter

TL;DR

This paper investigates the semi-classical gravitational collapse of a quantized matter shell, demonstrating how back-reaction effects slow down collapse near the horizon through numerical analysis.

Contribution

It develops an effective Lagrangian for a quantized matter shell and applies semi-classical and adiabatic methods to analyze back-reaction effects during collapse.

Findings

Back-reaction slows down collapse near the horizon.

Quantization affects the dynamics of gravitational collapse.

Numerical integration illustrates the impact of matter creation on collapse speed.

Abstract

The semi-classical 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 semi-classical 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.