Spherically symmetric collapse in quantum gravity

Abstract

The problem of classical singularities is revised on the basis of the quantum-gravity effective equations. We find a simple rule for establishing the Birkhoff theorem in spherically symmetric problems. All exact solutions of the lagrangian with C 2 αβγσ are obtained. Spherically symmetric collapse of the thin null shell of mass M is considered in the framework of a local theory describing vacuum polarization effects. The boundary-value problem is set and the asymptotic solution is obtained. It is found that the shell collapses to r = 0 without the rise of a singularity, and begins expanding. The global behaviour of the solution is obtained for small M. For large M it is conjectured that the event horizon does not form, and the apparent horizon is closed. An object forms, possessing the observable properties of a black hole, but living a finite time.