https://doi.org/10.1140/epjc/s10052-017-4663-6
Regular Article - Theoretical Physics
Analytic rotating black-hole solutions in N-dimensional f(T) gravity
1
Centre for Theoretical Physics, The British University in Egypt, P.O. Box 43, 11837, Cairo, Egypt
2
Faculty of Science, Mathematics Department, Ain Shams University, Cairo, Egypt
3
Egyptian Relativity Group (ERG), Cairo, Egypt
* e-mail: nashed@bue.edu.eg
Received:
31
October
2016
Accepted:
31
January
2017
Published online:
11
February
2017
A non-diagonal vielbein ansatz is applied to the N-dimension field equations of f(T) gravity. An analytical vacuum solution is derived for the quadratic polynomial 
and an inverse relation between the coupling constant 
and the cosmological constant 
. Since the induced metric has off-diagonal components, it cannot be removed by a mere coordinate transformation, the solution has a rotating parameter. The curvature and torsion scalars invariants are calculated to study the singularities and horizons of the solution. In contrast to general relativity, the Cauchy horizon differs from the horizon which shows the effect of the higher order torsion. The general expression of the energy-momentum vector of f(T) gravity is used to calculate the energy of the system. Finally, we have shown that this kind of solution satisfies the first law of thermodynamics in the framework of f(T) gravitational theories.
© The Author(s), 2017
