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arXiv · 1307.6652

Three dimensional stationary cyclic symmetric Einstein-Maxwell solutions; energy, mass, momentum, and algebraic tensors characteristics

Alberto A. Garcia-Diaz
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Abstract

The main purpose of this contribution is to determine physical and geometrical characterizations of whole classes of stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional gravity. The physical characterization is based on the determination of the local and global energy-momentum-mass quantities using the Brown-York approach. As far as to the algebraic-geometrical characterization is concerned, the eigenvalue problem for the electromagnetic field, energy-momentum and Cotton tensors is solved and their types are established. The families of Einstein-Maxwell solutions to be considered are: all uniform electromagnetic solutions possessing electromagnetic fields with vanishing covariant derivatives (stationary uniform and spinning Clement classes), all fields having constant electromagnetic field and energy-momentum tensors' invariants (Kamata-Koikawa solutions), the whole classes of hybrid electromagnetic Ayon-Cataldo-Garcia solutions, a new family of stationary electromagnetic solutions, the electrostatic and magnetostatic solutions with Peldan limit, the Clement spinning charged metric, the Martinez-Teitelboim-Zanelli black hole solution, and Dias-Lemos electromagnetic solution.

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Alberto A. Garcia-Diaz. 2013-07-25. Three dimensional stationary cyclic symmetric Einstein-Maxwell solutions; energy, mass, momentum, and algebraic tensors characteristics. https://arxiv.org/abs/1307.6652

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