Spherically symmetric solution in f(T) gravity

Abstract

In this study, we derive an exact spherically symmetric black hole solution within the gravitational theory defined by $f\left(T\right)=T+\frac{\zeta }{2}{T}^2$ where $\zeta$ has the dimension of $T^{-1}$ and $T$ represents the scalar torsion tensor. A key feature of the tetrad ansatz used here is that it eliminates all off-diagonal components of the field equations, unlike the most of previous approaches. The solution depends on the parameter $\zeta$ and does not reduce to the Schwarzschild spacetime as $\zeta \to 0$. Furthermore, since $\zeta$ cannot be zero, this solution is inherently novel within the framework of o$f\left(T\right)$ theory. We demonstrate that the curvature invariants of this solution exhibit milder singularities compared to those of the Schwarzschild solution. Additionally, we analyze its thermodynamic properties, showing that all derived quantities align well with established results in the literature.