Schwarzschild-NUT solution in modified teleparallel gravity theory

Spherically symmetric tetrad field is applied to the field equation of modified teleparallel gravity theory. Some constraints are assumed on the resulting non-linear partial differential equations. Exact vacuum solution is derived with two constants of integration. The derived solution has a vanishing scalar torsion, i.e., T=TμνλSμνλ=0 and its space-time is axially symmetric. It is shown that this solution can be rewritten as a product of three matrices, two local Lorentz transformations and one diagonal tetrad field. The local Lorentz transformations represent “so(3)” and a boost transformation and the diagonal tetrad reproduce the same metric field of the original tetrad.