Exhibiting Singularity-Free Ultra-Compact Stellar Models in Teleparallel \(f(\mathfrak{T})\) Gravity Under the MIT Bag \(EoS\)

Abstract In this paper, a relativistic model of anisotropic strange quark stars in the context of teleparallel $f(\mathfrak{T})$ gravity is presented, considering the fluid distribution in the interior of the star to be anisotropic. The analysis starts with the modified gravitational field equations in the light of a linear $f(\mathfrak{T})$ model in the context of static spherically symmetric spacetime geometry. Physically viable solutions are obtained by making use of the interior configuration modeled with the MIT bag model equation of state and the Finch--Skea spacetime ansatz, to get a self-consistent stellar solution. The exterior Schwarzschild spacetime is smoothly matched with the interior geometry at the stellar boundary, thus the model parameters can be determined by means of the continuity conditions. The obtained solution is further explored by different thermodynamic, energy and stability criteria on physical viability. It is applied to observational relevance, for compact stars SAX~J1808.4$-$3658 and 4U~1608$-$52. The derived solutions show that under appropriate parameter choices of the $f(\mathfrak{T})$ model, the proposed strange quark star configuration may be realized with higher value of the mass and compactness, which may have implications in the astrophysics in the context of modified teleparallel gravity. \textbf{\color{blue}The results indicate that \(f(\mathfrak{T})\) gravity can provide an effective description equivalent to General Relativity, accompanied by a modified coupling and a constant geometric contribution, thereby offering a possible framework for exploring the behavior of highly compact strange quark stars.}