Formation of regular black hole from baryonic matter

Abstract

We present a family of exact, singularity-free solutions describing the collapse of baryonic matter characterized by a barotropic equation of state whose coefficient $\alpha(r,v)$ varies in both radius and time. By matching these interior solutions to the Husain exterior metric, we obtain a self-consistent, dynamical spacetime representing a regular black hole. Although the pressure profile of our models grows with radius and eventually violates the dominant energy condition beyond a critical surface-necessitating an external junction to ensure a globally well-defined spacetime-the interior solution remains non-singular throughout the collapse. We further analyze the optical properties of these regular black holes and find that both the photon sphere radius and the corresponding shadow radius increase monotonically as the local equation of state parameter $\alpha$ is raised. Moreover, the matching interface between the interior and exterior metrics naturally suggests a phase transition in the collapsing fluid, which can postpone the formation of an apparent horizon. Taken together, our results not only highlight novel physical features of horizon formation in regular collapse models but also identify characteristic shadow signatures that could be tested by future observations.