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

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 ${\overline{\eta }}_{\mathrm{ij}}$ to derive complicated rotating solutions. In the other procedure, discussed in this work, one selects a diagonal Minkowskian metric ${\eta }_{\mathrm{ij}}$ to derive much simpler and appealing rotating solutions. We also show that if ( ${g}_{\mu \nu },\phantom{\rule{0.166667em}{0ex}}{\eta }_{\mathrm{ij}}$ ) is a rotating solution then ( ${\overline{g}}_{\mu \nu },\phantom{\rule{0.166667em}{0ex}}{\overline{\eta }}_{\mathrm{ij}}$ ) is a rotating solution too with similar geometrical properties, provided ${\overline{\eta }}_{\mathrm{ij}}$ and ${\eta }_{\mathrm{ij}}$ are related by a symmetric matrix R: ${\overline{\eta }}_{\mathrm{ij}}={\eta }_{\mathrm{ik}}{R}_{\mathrm{kj}}$ .