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In this paper we study properties that the vacuum must possess in the minimalextension to the teleparallel equivalent of general relativity (TEGR) where theaction is supplemented with a quadratic torsion term. No assumption is madeabout the weakness of the quadratic term although in the weak-field regime thevalidity of our previously derived perturbative solution is confirmed.Regarding the exact nature of the vacuum, it is found that if the center ofsymmetry is to be regular, the mathematical conditions on the tetrad at theisotropy point mimic those of general relativity. With respect to horizons itis found that, under very mild assumptions, a smooth horizon cannot existunless the quadratic torsion coupling, $\alpha$, vanishes, which is the TEGRlimit (with the Schwarzschild tetrad as its solution). This analysis is thensupplemented with computational work utilizing asymptotically Schwarzschildboundary data. It is verified that in no case studied does a smooth horizonform. For $\alpha > 0$ naked singularities occur which break down the equationsof motion before a horizon can form. For $\alpha < 0$ there is a limited rangeof $\alpha$ where a vacuum horizon might exist but, if present, the horizon issingular. Therefore physically acceptable black hole horizons are problematicin the studied theory at least within the realm of vacuum static sphericalsymmetry. These results also imply that static spherical matter distributionsgenerally must have extra restrictions on their spatial extent andstress-energy bounds so as to render the vacuum solution invalid in thesingular region and make the solutions finite.

On spherically symmetric vacuum solutions and horizons in covariant $f(T)$ gravity theory