Black hole solutions surrounded by anisotropic fluid in f(T,T) gravity

In this work, we investigate some extensions of the Kiselev black hole solutions in the context of $f(\mathbb{T},\CMcal{T})$ gravity. By mapping the components of the Kiselev energy-momentum tensor into the anisotropic energy-momentum tensor and assuming a particular form of $f(\mathbb{T},\CMcal{T})$, we obtain exact solutions for the field equation in this theory that carries dependence on the coupling constant and on the parameter of the equation of state of the fluid. We show that in this scenario of modified gravity some new structure is added to the geometry of spacetime as compared to the Kiselev black hole. We analyse the energy conditions, mass, horizons and the Hawking temperature considering particular values for the parameter of the equation of state.