The Electrically Charged Extreme BTZ Black Hole with Self (Anti-self) Dual Maxwell Field
Mauricio Cataldo, Patricio Salgado
Abstract
Recently M. Kamata and T. Koikawa claimed to obtain the charged version of the spinning BTZ black hole solution by assuming an (anti-) self dual condition imposed on the orthonormal basis components of the electric and magnetic fields. We point out that the Kamata-Koikawa field is not a solution of the Einstein-Maxwell equations and we find the correct solution of the studied problem. It is shown that a duality mapping exists among spinning solutions obtained from electrostatic and magnetostatic fields with the help of the local transformation t t-ωθθ θ-ωt.
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