Causal structure of nonhomogeneous dust collapse in effective loop quantum gravity

Abstract

We study the causal structure for spherically symmetric dust collapse within a model of effective loop quantum gravity in midisuperspace framework. We develop a general strategy (working beyond the dynamical model of our consideration) for constructing double null coordinates, allowing the extraction of conformal diagrams within single coordinate charts. With the methods introduced, we confirm that the homogeneous Oppenheimer-Snyder collapse scenario resembles the Reissner-Nordström-like picture. For the nonhomogenous collapse scenario, we construct the conformal diagrams, subsequently, we study its relevant properties, in particular, dust particles' trajectories, apparent horizons and shell-crossing singularities. We conclude that a significant region of spacetime remains inaccessible to the model's dynamics due to the formation of the shell-crossing singularities. The question of whether a timelike singularity, similar to that in the homogeneous dust ball collapse scenario, arises in the nonhomogeneous case remains unresolved. Furthermore, we find that phenomena such as black hole explosions or gravitational shock waves cannot be witnessed by an external observer who does not cross any horizon. Indeed, the collapse cannot take place within single asymptotic region.

v3: revised version accepted for publication in PRD, 23 pages, 9 figures

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