Causal Structure of a recent Loop Quantum Gravity Black Hole Collapse Model

Abstract

The causal structure of the recent loop quantum gravity black hole collapse model [1] is analysed. As the spacetime is only approximately diffeomorphism invariant up to powers of , it is not straight forwardly possible to find global conformally compactified coordinates and to construct the Penrose diagram. Therefore, radial in-and outgoing light rays are studied to extract the causal features and sketch a causal diagram. It was found that the eternal metric [2], which is the vacuum solution of the collapse model, has a causal horizon. However, in the collapsing case light rays travel through matter to causally connect the regions in-and outside the horizon -the causal horizon is not present in the collapsing scenario. It is worked out that this is related to the shock wave and spacetime discontinuity, which allows matter travelling super-luminal along a space-like trajectory from the vacuum point of view, but remaining time-like from the matter perspective. The final causal diagram is a nice compact patch of a Reissner-Nordström causal diagram. Further, possibilities of a continuous matter collapse with only time-like evolution are studied. It was found that the time-reversed vacuum metric is also a solution of the dynamical equations and a once continuously differentiable matching of the vacuum spacetime across the minimal radius is possible. This allows an everywhere continuous and time-like collapse process at the cost of an infinite extended causal diagram. This solution is part of an infinitely extended eternal black hole solution with a bounce, whose global extension is constructed. Due to the analysis of radial light rays, it is possible to sketch causal diagrams of these spacetimes.

On the fate of quantum black holes

“…The conformal diagram for the effective vacuum solution has already been studied in considerable detail [109], but there are some important differences in the conformal diagram once matter (in this case dust) is included. For concreteness, we will sketch the conformal diagram for the Oppenheimer-Snyder collapse model derived in Sec.…”