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

arXiv comment5 twocolumn pages, to appear in the European Physical Journal C

References in corpus (9)

• Cylindrical Black Hole in General Relativity
• The covariant formulation of f(T) gravity
• Rotating Charged Black Strings in General Relativity
• Higher Dimensional Charged Rotating Solutions in (A)dS Space-times
• Spin Connection and Renormalization of Teleparallel Action
• Rotating AdS black holes in Maxwell-$f(T)$ gravity
• $D$-dimensional charged Anti-de-Sitter black holes in $f(T)$ gravity
• Rotating and non-rotating AdS black holes in $f(\mathcal{T})$ gravity non-linear electrodynamics
• Rotating charged AdS solutions in quadratic $f(T)$ gravity

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• Generalized Hidden Conformal Symmetry in Quadratic $f(T)$ Gravity
• Exact Analytical Taub-NUT like Solution in f(T) Gravity
• New Rotating Black Hole Solutions With Imperfect Fluid Energy-Momentum Tensor In $f(R)$ Gravity
• New Lorentzian Taub-NUT and Euclidean Eguchi-Hanson Solutions in $f(R)$ gravity