Dynamical singularity resolution in spherically symmetric black hole formation

We study numerically the effects of loop quantum gravity motivated corrections on massless scalar field collapse in Painlevé-Gullstrand coordinates. Near criticality the system exhibits Choptuik scaling with a mass gap and a new scaling relationship dependant upon the quantum length scale. Classical singularities are resolved by a radiationlike phase in the quantum collapse: the black hole consists of a compact region of spacetime bounded by a single, smooth trapping horizon. The “evaporation” is not complete but leaves behind a small expanding shell that disperses to infinity.

Figure 1

A comparison of $f_{\mathrm{unreg}}(r)$, $f_{\mathrm{reg}}(r)$, and $f_{\mathrm{smooth}}(r)$ with $\mu =0.1$.

Figure 2

Mass scaling for varied $A$ in Gaussian initial data ($\Delta r={10}^{-4}$ near the origin). All curves are similar for large $A$; as $A$ is decreased, each curve stops at some value of $A=A_{q*}$. $A_{q*}$ is bigger for curves with larger $\mu$.

Figure 3

Variation in the parameter $A$ in tanh initial data.

Figure 4

Classical spacetime diagram. The (black) solid lines are null geodesics and the (red) dashed lines indicate the trapping surface boundary.

Figure 5

Quantum spacetime diagram. The (black) solid lines are null geodesics and the (red) dashed lines indicate the trapping surface boundary.