Analytic rotating black-hole solutions in N-dimensional f(T) gravity

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 f ( T ) = T + ϵ T 2 and an inverse relation between the coupling constant ϵ and the cosmological constant Λ . 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.