Kerr–Newman-NUT Black Hole in f(T) Gravity Theory and Its Thermodynamical Quantities

Abstract

We show by explicit calculations that any general relativity solution remains a solution in f(T) gravitational theories provided some constraints on f(T) and its first derivatives are satisfied. This is done by applying an axially-symmetric tetrad field to the charged field equation of f(T), where \(T = T^{\mu }_{\nu \lambda }S_{\mu }^{\nu \lambda }\) is the scalar torsion tensor, gravity theory. In the linear case, f(T) = T which corresponds to general relativity theory, we derive solution with four constants of integration. For the non-linear case, we substitute the derived solution in the tetrad field and change the azimuthal coordinate to be a function of r, θ and ϕ, i.e., \(\Phi = L(r,\theta ,\phi )\). We calculate the scalar torsion and its derivatives then, a condition one the scalar torsion to be constant is assumed. We derive the value of \(L(r,\theta ,\phi )\) which satisfies this condition. The associated metric of the derived solution is shown to be a charged Kerr-NUT space time. The energy of this solution is calculated using the Euclidean continuation method and a consistent value is derived. We also calculate the thermodynamical quantities of charged Kerr-NUT space time and investigate the first law of thermodynamics and quantum statistical relation.