The effect of modified hybrid and logarithmic teleparallel gravity on the interior solutions of compact stars

This study aims to investigate spherically symmetric anisotropic solutions that describe compact stellar objects in the modified Rastall teleparallel (MRT) theory of gravity. In order to achieve this goal, we utilize the Karmarkar condition to evaluate the spherically symmetric components of the line element. We explore the field equations by selecting appropriate off-diagonal tetrad fields for two different scenarios. In the first scenario, we use a hybrid form of f(T) = βe${}^{mT}$ T${}^n$ and a linear equation of state (EoS) p${}_r$ = ξρ+ϕ, where 0 < ξ < 1, to evaluate h(T). In the second scenario, we again use a hybrid form of f(T) = βe${}^{mT}$ T${}^n$ and a logarithmic form of h(T) = ψ log(ϕT${}^{\chi }$). We aim to investigate the possible forms of gravity modifications by evaluating the function for different values of m and n, reducing the gravity forms to hybrid, power law form, and exponential form. Our findings reveal that the exponential-logarithmic case is unstable in our scenario. To the best of our knowledge, we are the first to attempt to explore compact star models in MRT gravity. After obtaining the field equations, we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models. We utilize observational data, such as the mass and radius of the PSRJ 1416-2230 model, to ensure the physical plausibility of our findings.