Singularity resolution and regular black hole formation in gravitational collapse in asymptotically safe gravity

Abstract

We adopt an effective action inspired by asymptotically safe gravity, in which the effective gravitational constant is parametrized as $G(\epsilon) = G_{N} /[1 + \tilde{\omega} (G_{N}^{2} \epsilon)^{\alpha}]$, where $G_{N}$ and $\epsilon$ denote Newton's gravitational constant and the energy density of the matter field, respectively, with two dimensionless model parameters, $\tilde{\omega}$ and $\alpha$. Within this framework, we investigate the complete gravitational collapse of a homogeneous ball of perfect fluid and find that singularity is completely resolved for $\alpha > 1$ but not for $1/2 \le \alpha \le 1$. The case of $0 < \alpha < 1/2$ is inconsistent with asymptotic safety. Moreover, we note that although the singularity cannot be fully resolved for $\alpha = 1$, it is significantly weakened by quantum gravity effects. Furthermore, we successfully construct a static exterior metric which, together with the interior solution, describes the dynamical formation of regular black holes in an asymptotically flat spacetime. The resulting regular black hole, obtained as the final static state, contains a de Sitter core and admits a static metric fully expressible in terms of the Lerch transcendent for general cases and in elementary functions for certain values of $\alpha$, including $\alpha = 2$. We also discuss the formation of gravastars and the late-time evaporation process of the regular black holes.