Regular black hole from regular initial data

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 [Formula: see text] as a limiting case of the time-evolving (nonstationary) spacetime [Formula: see text]. In the spirit of P. S. Joshi, D. Malafarina and R. Narayan, Class. Quantum Grav. 31 (2014) 015002, 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 [Formula: see text] and [Formula: see text] in the sense that [Formula: see text], the causal past of p does not intersect [Formula: see text]. While the classic Oppenheimer–Snyder collapse model necessarily produces a black hole with a Schwarzschild singularity at the center, we show here that there are classes of regular initial conditions for which the collapse gives rise to a RBH.