On "Rotating charged AdS solutions in quadratic $f(T)$ gravity": New rotating solutions

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) \textbf{79}:668, one uses a non-trivial, non-diagonal, Minkowskian metric ${\bar{\eta }}_{ij}$ to derive complicated rotating solutions. In the other procedure, discussed in this work, one selects a diagonal Minkowskian metric ${\eta }_{ij}$ to derive much simpler and appealing rotating solutions. We also show that if ($g_{\mu \nu },{\eta }_{ij}$) is a rotating solution then (${\bar{g}}_{\mu \nu },{\bar{\eta }}_{ij}$) is a rotating solution too with similar geometrical properties, provided ${\bar{\eta }}_{ij}$ and ${\eta }_{ij}$ are related by a symmetric matrix $R$: ${\bar{\eta }}_{ij}={\eta }_{ik}{R}_{kj}$.

5 twocolumn pages, to appear in the European Physical Journal C