Hyperscaling violating black holes in scalar-torsion theories

TL;DR

This paper explores a scalar-torsion gravity theory that yields novel black hole solutions with hyperscaling violating Lifshitz asymptotics, finite energy density at the horizon, and potential astrophysical implications such as light deflection.

Contribution

It introduces a new class of black hole solutions in scalar-torsion theories with non-minimal derivative coupling, expanding the understanding of teleparallel gravity models.

Findings

Found static spherically symmetric black hole solutions with hyperscaling violating Lifshitz asymptotics.

Scalar field diverges at the horizon but energy density remains finite.

Solutions suggest additional light deflection compared to Newtonian predictions.

Abstract

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.