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In this paper we consider a class of static spacetimes in higher dimensional($D \ge 4$) scalar-torsion theories with non-minimal derivative coupling andthe scalar potential turned on. The spacetime is conformal to a product spaceof a two-surface and a $(D-2)$-dimensional submanifold. Analyzing the equationsof motion in the theory we find that the $(D-2)$-dimensional submanifold has toadmit constant triplet structures in which the torsion scalar is one of them.This implies that these equations of motion can be simplified into a singlehighly non-linear ordinary differential equation called the master equation.Then, we show that in this case the solution admits at least a nakedsingularity at the origin which is not a black hole. In the asymptotic region,the spacetimes converge to spaces of constant scalar curvature which aregenerally not Einstein. We also use perturbative method to linearize the masterequation and construct the first order solutions. At the end, we establish theanalysis of local-global existences of the master equation and then, prove thenon-existence of regular global solutions.

Static Spacetimes In Higher Dimensional Scalar-Torsion Theories With Non-Minimal Derivative Coupling