Probing black hole evolution through homogeneous gravitational collapse in f(Q) gravity

Abstract

In this study, we investigate black hole (BH) formation resulting from the gravitational collapse of self-gravitating systems within the context of $f\left(Q\right)$ gravity. This work addresses key unresolved issues in theoretical physics regarding the end stage of gravitational collapse in massive stars. Building on the foundational research of Oppenheimer and Snyder (1939), we analyze a homogeneous collapsing system with perfect fluid distributions under $f\left(Q\right)=Q+\alpha Q^2$ gravity theory. To achieve this, we consider a homogeneous collapsing system with a spherically symmetric space–time geometry described by the FLRW metric with prefect fluid matter distribution. We have also discussed the junction conditions $f\left(Q\right)$ theory. By employing a parametrization of the expansion scalar, we derive an exact, model-independent solution to the Einstein field equations for the collapsing system. To explore the physical viability of the model we consider some known massive stars- $R136a3,R136c$, and $R99$ with their known astrophysical stellar data (masses and radii). We discuss the formation of apparent horizon and space–time singularity, which further predicts BH as the final state of these collapsing stars. Additionally, we calculate the lifespans of these stellar objects, showing that higher-mass stars have shorter lifespans compared to less massive stars. We have also applied various test, including energy conditions, the equation of state, and stability criteria, and the adiabatic index. We have also presented a comparative analysis of our solution with standard Einstein’s General Relativity.