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

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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 $t\longrightarrow t-ωθθ\longrightarrow θ-ωt.$
11 pages, Latex. Submitted to Phys. Lett. B

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General Relativity and Quantum Cosmology

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http://salesiana.dossiersoluciones.com/handle/123456789/35830

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/gr-qc/9611004
 http://arxiv.org/abs/gr-qc/9611004

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arXiv