Maximum Mass Limit of Generalized MIT Compact Star: A Theoretical Study of Thin Shell Dynamics and Gravitational Lensing

In this study, the properties, equilibrium, and stability of compact objects within the framework of teleparallel gravity with the generalized MIT bag model are investigated. By incorporating the modified field equations, the influence of the generalized bag constant on the structure and physical characteristics of quark stars and neutron stars is analyzed. A key focus of the work is the examination of the Israel junction conditions for the first time in the literature, which are employed to study the stability of the thin-shell interface separating the interior quark matter from the exterior vacuum or surrounding medium. A detailed stability analysis is conducted by evaluating the adiabatic index, Herrera's cracking criteria to determine the viability of the interior stellar configurations. To validate results, the predictions of our extended MIT Bag model are compared with observational constraints, including the compact object detected in GW190814, whose mass lies within the range of $2.5-2.67M_{\odot }$. Furthermore, our findings with well-documented neutron stars (NSTRs) are compared, such as 4U 1608-52 $\left(1,.,{74}_{-0.14}^{+0.14},,M_{\odot }\right)$ and PSR J0952-0607 $\left(2,.,{35}_{-0.17}^{+0.17},,M_{\odot }\right)$. Additionally, the gravitational lensing effects caused by the thin shell are explored, which provide insight into the observational signatures of these compact objects. The stability of the thin shell using thermodynamic relations is also commented on. A comprehensive understanding of the equilibrium and stability conditions governing compact stars in modified gravity is offered by the results, with significant implications for the equation of state of high-density matter. Furthermore, the phenomenological and observational properties of relativistic astrophysical objects are explored.