Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity

Understand

We study various forms of diagonal tetrads that accommodate Black Hole solutions in $f(T)$ gravity with certain symmetries.

• As is well-known, vacuum spherically symmetric diagonal tetrads lead to rather boring cases of constant torsion scalars.
• We extend this statement to other possible horizon topologies, namely, spherical, hyperbolic and planar horizons.
• All such cases are forced to have constant torsion scalars to satisfy the anti-symmetric part of the field equations.