On ‘rotating charged AdS solutions in quadratic f(T) gravity’: new rotating solutions

Abstract

Abstract We show that there are two or more procedures to generalize the known four-dimensional transformation, aiming to generate cylindrically rotating charged exact solutions, to higher dimensional spacetimes . In the one procedure, presented in Eur. Phys. J. C (2019) 79:668, one uses a non-trivial, non-diagonal, Minkowskian metric $$\bar{\eta }_{ij}$$ η ¯ ij to derive complicated rotating solutions. In the other procedure, discussed in this work, one selects a diagonal Minkowskian metric $${\eta }_{ij}$$ η ij to derive much simpler and appealing rotating solutions. We also show that if ( $$g_{\mu \nu },\,\eta _{ij}$$ g μ ν , η ij ) is a rotating solution then ( $$\bar{g}_{\mu \nu },\,\bar{\eta }_{ij}$$ g ¯ μ ν , η ¯ ij ) is a rotating solution too with similar geometrical properties, provided $$\bar{\eta }_{ij}$$ η ¯ ij and $${\eta }_{ij}$$ η ij are related by a symmetric matrix R: $$\bar{\eta }_{ij}={\eta }_{ik}R_{kj}$$ η ¯ ij = η ik R kj .