A new perspective on gravitational collapse: a comprehensive analysis using $$\Theta $$ parametrization

Abstract In this article, we have studied some new facets of gravitational collapse, beyond conventional notions of black holes, and naked singularities. The present work is focused on the unresolved problems of theoretical physics concerning the final fate of the gravitational collapse of any massive star. By generalizing the foundational work of Oppenheimer and Snyder (Phys Rev 56:455, 1939), we have considered the homogeneous gravitational collapsing system filled with perfect fluid distributions (devoid of dust fluid) within the framework of GR theory. The article investigates a homogeneous gravitational collapsing system using a parametrization scheme for the expansion-scalar $$(\Theta )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Θ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and determining the exact solution of field equations. Further, by employing the known Darmois–Israel boundary condition, we have discussed the solution in more detail, and the model’s physical and geometrical quantities are obtained in terms of stellar mass ( M ), making it crucial for astrophysical applications. To assess the astrophysical viability of our model, we consider a massive star- $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> Canis Majoris and throughout this study we have presented a detailed numerical and graphical analysis of our model. The analysis of singularities in the models is conducted through the examination of the apparent horizon. Our findings demonstrate that the star continues to collapse indefinitely in co-moving time, ultimately leading to a space-time singularity-this represents a case of continuous gravitational collapse. We propose that this scenario describes an “Eternal Collapsing Object,” which may be treated as a “mathematical black hole without any finite equilibrium state.” Our presented models undergo rigorous physical tests to ensure their regularity, causality, and stability, and to satisfy the necessary energy conditions.