  We study a gravity theory where a scalar field with potential, beyond its
minimal coupling, is also coupled through a non-minimal derivative coupling
with the torsion scalar which is the teleparallel equivalent of Einstein
gravity. This theory provides second order equations of motion and we find
large-distance non-perturbative static spherically symmetric four-dimensional
solutions. Among them a general class of black hole solutions is found for some
range of the parameters/integration constants with asymptotics of the form of
hyperscaling violating Lifshitz spacetime with spherical horizon topology.
Although the scalar field diverges at the horizon, its energy density and
pressures are finite there. From the astrophysical point of view, this solution
provides extra deflection of light compared to the Newtonian deflection.

High Energy Physics - Theory;General Relativity and Quantum Cosmology