Anisotropic configurations of new class of compact stars in modified teleparallel gravity

This paper provides modeling of compact stars in the framework of modified teleparallel gravity theory. The f(T) gravity mechanism employs torsion rather than spacetime curvature to explain gravitational phenomena analogous to general relativity. In this study, we developed new compact stars solutions by evaluating the \(g_{tt}\) components of the spherically symmetric interior geometry by using the f(T) gravity field equations and linear equation of state. Further, we also evaluated the exterior solution from the available set of field equations rather than matching with the Schwarzschild solution or any other available exterior geometry. The physical parameters of the model are analyzed graphically by using observational data of four prominent compact stars \(SAX\; J1808.4-3658,\; Vela\; X-1,\; PSR\; J1614-2230,\; \text {and}\; PSR\; J0952-0607\). This viable study of compact objects includes the investigation of metric potential functions, energy density, equation of state, radial and tangential pressures, as well as their anisotropic effects. The Tolman–Volkoff equation (TOV) verifies the hydrostatic equilibrium, and it is also verified that all the standard energy conditions are satisfied in the stellar interior. Moreover, the causality condition is satisfied through analysis of sound speed and adiabatic index which lie in a stable regime, and therefore, the model proposed is physically viable and stable. This study explores how gravitational redshift behaves, and proposes explanations regarding stellar compactness and mass functions, and checks gradients spanning through the star radius. We observed that very close to the boundary, trace energy condition, dominant energy condition, and Abreu criteria show the instability for some compact star candidates; otherwise, as a whole, our proposed model is stable and physical. The studied gravity model meets all the physical and stability criteria, which verify that stellar configurations present realistic and uniform behavior. The research validates f(T) gravity as an effective theory to simulate compact astrophysical objects with valuable insights into gravity behavior in strong-field situations.