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 $λ$ embedded in the inhomogeneity of the conformal factor of the interior metric. Examples with $λ< 0$ enforce an eventual collapse to singularity and $λ> 0$ cases produce a non-singular collapse resulting in a loop-quantum-corrected Schwarzschild geometry modulo a conformal factor. Interestingly, for $λ< 0$ 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 $λ<0$ 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 $λ$. 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.

Figures (33)

• Figure 1: Case I - Evolution of the temporal part of the conformal factor, $T(t)$ with $t$ for different values of $\alpha$ where we have chosen $r_0=4$.
• Figure 2: Case I - Evolution of the energy density, $\rho$ with $t$ at different regions characterized by different values of $r$, with $r_0=4,\alpha=1$.
• Figure 3: Case I - Plot of the energy density profile $\rho(r)$ for different instants of time $t$, with $r_0=4$, $\alpha=1$.
• Figure 4: Case I - Evolution of the energy density, $\rho$ with $t$ at different regions characterized by different values of $r$, with $r_0=4,\alpha=2$.
• Figure 5: Case I - Evolution of the energy density, $\rho$ with $t$ at different regions characterized by different values of $r$, with $r_0=4,\alpha=2$.