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The Electrically Charged Extreme BTZ Black Hole with Self (Anti-self) Dual Maxwell Field

Mauricio Cataldo·Patricio Salgado
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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 $t\longrightarrow t-ωθθ\longrightarrow θ-ωt.$

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Mauricio Cataldo, Patricio Salgado. 1996-11-04. The Electrically Charged Extreme BTZ Black Hole with Self (Anti-self) Dual Maxwell Field. https://arxiv.org/abs/gr-qc/9611004

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