The fate of a Quantum-Corrected Collapsing Star in General Relativity

Abstract

We incorporate some corrections inspired by loop quantum gravity into the concept of gravitational collapse and propose a complete model of the dynamic process. The model carries the essence of a mass-independent upper bound on the curvature scalars originally found as a crucial feature of black holes in loop quantum gravity. The quantum-inspired interior is immersed in a geometry filled with null radiation and they are matched at a distinct boundary hypersurface. The ultimate fate of the process depends on inhomogeneities of the metric tensor cofficients. We find a critical parameter $\lambda$ embedded in the inhomogeneity of the conformal factor of the interior metric. Examples with $\lambda <0$ enforce an eventual collapse to singularity and $\lambda >0$ cases produce a non-singular collapse resulting in a loop-quantum-corrected Schwarzschild geometry modulo a conformal factor. Interestingly, for $\lambda <0$ as well, there exist situations where the quantum effects are able to cause a bounce but fall short of preventing the ultimate formation of singularity. The trapped surface formation condition is studied for $\lambda <0$ case to infer about the visibility of the final singularity. Interestingly, we find a possibility of formation of three horizons during the course of the collapse. Eventually all of them merge into one single horizon which envelopes the final singularity. For the non-singular case, there is a possibility that the sphere can evolve into a wormhole throat whose radius is found to be inversely proportional to the critical parameter $\lambda$. Depending on the nature of evolution and the shell regions, the collapsing shells violate some standard energy conditions which can be associated with the quantum inspired corrections.

arXiv comment31 pages, 33 figures, Comments are welcome

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