Spherically symmetric vacuum solutions and horizons in covariant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> gravity theory

In this paper we study properties that the vacuum must possess in minimal extension to teleparallel equivalent of general relativity (TEGR) where action is supplemented with a quadratic torsion term. No assumption made about weakness term although weak-field regime validity our previously derived perturbative solution confirmed. Regarding exact nature vacuum, it found if center symmetry be regular, mathematical conditions on tetrad at isotropy point mimic those relativity. With respect horizons that, under very mild assumptions, smooth horizon cannot exist unless coupling, $\alpha$, vanishes, which TEGR limit (with Schwarzschild as its solution). This analysis then computational work utilizing asymptotically boundary data. It verified no case studied does form. For $\alpha > 0$ naked singularities occur break down equations motion before can < there limited range $\alpha$ might but, present, singular. Therefore physically acceptable black hole are problematic theory least within realm static spherical symmetry. These results also imply matter distributions generally have extra restrictions their spatial extent and stress-energy bounds so render invalid singular region make solutions finite.