Black hole formation in gravitational collapse and their astrophysical implications

In this study, we have explored the process of black hole (BH) formation occurring in the collapse of a self-gravitating configuration using an innovative approach. The exact solution of the Einstein field equations is obtained in a model-independent way by considering a parametrization of the expansion scalar (Theta) in the background of spherically symmetric space-time geometry governed by the FLRW metric. Smooth matching of the interior solution with the Schwarzschild exterior metric across the boundary hypersurface of the star, together with the condition that the mass function m(t, r) is equal to Schwarzschild mass M, is used to obtain all the physical and geometrical parameters in terms of the stellar mass. The four known massive stars namely R136a3, Melnick, R136c, and R136b with their known astrophysical data (mass, radius, and present age) are used to study the physics of the model both numerically and graphically. We demonstrate that the formation of the apparent horizon occurs earlier than the singular state that is, the collapse of massive stars in our model results in the eventual formation of black holes as their final state. We have conducted an analysis indicating that the lifespans of massive stars are closely related to their respective masses. Our findings demonstrate that more massive stars exhibit considerably shorter lifespans in comparison to their lighter counterparts. Thus, the presented model corresponds to the evolutionary stages of astrophysical stellar objects and theoretically predicts their possible lifespan. We have also shown that our model satisfies the energy conditions and stability requirements via Herrera's cracking method.