Regular black hole from regular initial data

Abstract: Recently, there has been an interest in exploring black holes that are regular in the sense that the central curvature singularity is avoided. Here, we depict a method to obtain a regular black hole (RBH) spacetime from the unhindered gravitational collapse, beginning with regular initial data of a spherically symmetric perfect fluid. In other words, we obtain the equilibrium (static) spacetime $(\mathcal{M}, \Tilde{g})$ as a limiting case of the time-evolving (non-stationary) spacetime $(\mathcal{M}, g)$. In the spirit of Joshi, Malafarina and Narayan (\textit{Class. Quantum Grav. 31, 015002, 2014}), our description of gravitational collapse is implicit in nature in the sense that we do not describe the data at each time-slice. Rather, we impose a condition in terms of geometric and matter variables for the collapse to have an end-state that is devoid of incomplete geodesics but admits a marginally trapped surface (MTS). The admission of MTS causally disconnects two mutually exclusive regions $\Hat{\mathcal{M}}_1$ and $\Hat{\mathcal{M}}_2\subset \mathcal{M}$ in the sense that $\forall~p\in\Hat{\mathcal{M}_2}$, the causal past of $p$ does not intersect $\Hat{\mathcal{M}}_1$. While the classic Oppenheimer-Snyder collapse model necessarily produces a black hole with a Schwarzschild singularity at the centre, we show here that there are classes of regular initial conditions for which the collapse gives rise to a RBH.