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 $R$: $\bar{\eta}_{ij}={\eta}_{ik}R_{kj}$.