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

TL;DR

This paper compares two methods for generating higher-dimensional rotating charged solutions in quadratic f(T) gravity, highlighting a simpler approach using diagonal Minkowskian metrics and establishing conditions for solution equivalence.

Contribution

It introduces a simpler procedure for deriving higher-dimensional rotating solutions using diagonal Minkowskian metrics and relates solutions via symmetric transformations.

Findings

Two procedures for higher-dimensional rotating solutions are compared.

The simpler method uses diagonal Minkowskian metrics for solution generation.

Rotating solutions are related through symmetric metric transformations.

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