Anisotropic quintessence compact star in $f(T)$ gravity with Tolman-Kuchowicz metric potentials

Abstract To obtain analytically relativistic quintessence anisotropic spherical solutions in the $f(T)$ paradigm is the primary objective of this paper. To do this, the pressure anisotropy condition is imposed and we employ a metric potential of the Tolman-Kuchowicz type. We also suppose that our current model incorporates a quintessence field characterized by a parameter $\omega_q$, in addition to the anisotropic matter distribution. In the presence of the parameter $\alpha$, the field equations are modified by the choice of the $f (T)$ function. The $f(T)$ gravity parameter $\alpha$ adds new components to the basic physical characteristics, such as density, pressure, subliminal sound velocity, surface redshift, etc of the present model. By selecting the compact star Her X-1 and varying $\alpha$ from $0.5$ to $2.5$, we examined all the physical characteristics of the model parameter of the configuration. The graphical process demonstrates that a more compact item is produced with greater values of $\alpha$. The hydrostatic equilibrium condition of the model is discussed as well as the mass-radius relationship for our current model is obtained.