Gravitational collapse in effective loop quantum gravity: beyond marginally bound configurations

Abstract

We study gravitational collapse in effective loop quantum gravity, focusing on non-marginally bound configurations in Lemaître-Tolman-Bondi spacetimes. In the homogeneous limit we recover the effective dynamics of loop quantum cosmology for Friedman cosmologies with spatial curvature. We study a particular family of configurations with a homogeneous interior and a sharp boundary where the dust energy density rapidly and continuously decreases to zero. For these configurations, the gravitational collapse continues to the Planck regime when a bounce occurs, at which point the dust ball starts to expand, and a shock wave forms in the gravitational field within the order of a Planck time after the bounce. The shock slowly moves outwards, eventually reaching the horizon which then disappears, at which time there is no longer a black hole. If the initial configuration is bound, the shock asymptotes to a maximal radius, whereas for unbound initial configurations the shock escapes to infinity. In all cases, the black hole lifetime is proportional to the square of the black hole mass, and additionally depends on how strongly bound the dust profile is; this last quantity also affects the vacuum region outside the dust profile which is not solely determined by the black hole mass and charge as in spherically symmetric general relativity. We also use numerics to study a wide range of other types of initial configurations, both bound and unbound, with qualitatively similar results.