# General form of the analytic function f (T) in diverse dimension for a static planar spacetime

## Document Type

Article

## Publication Date

9-1-2019

## Abstract

© 2019 World Scientific Publishing Company. We derive an exact static solution in diverse dimension, without any constraints, to the field equations of f(T) gravitational theory using a planar spacetime with two unknown functions, i.e. b(r) and b1(r). The black hole solution is characterized by two constants, c1 and c2, one is related to the mass of the black hole, c1, and the other is responsible to make the solution deviate from the teleparallel equivalent of general relativity (TEGR). We show that the analytic function f(T) depends on the constant c2 and becomes constant function when c2 = 0 which corresponds to the TEGR case. The interesting property of this solution is the fact that it makes the singularity of the Kretschmann invariant much softer than the TEGR case. We calculate the energy of this black hole and show that it is equivalent to ADM mass. Applying a coordinate transformation, we derive a rotating black hole with nontrivial values of the torsion scalar and f(T). Finally, we examine the physical properties of this black hole solution using the laws of thermodynamics and show that it has thermodynamical stability.

## Recommended Citation

Nashed, Gamal, "General form of the analytic function f (T) in diverse dimension for a static planar spacetime" (2019). *Centre for Theoretical Physics*. 50.

https://buescholar.bue.edu.eg/centre_theoretical_physics/50