Exact solutions for a system of two counter-rotating black holes

The Bretón–Manko equatorially antisymmetric binary configuration revisited

“…In the absence of the electric charge Q (pure vacuum case) when the BM solution represents two counter-rotating Kerr sources [25] a similar problem was already solved in the paper [18] by introducing the Komar angular momentum per unit mass a instead of a ′ , and the coordinate distance R between the centers of the sources instead of k (see Fig. 1).…”

“…The BM solution gave rise to a systematic study of equatorially antisymmetric spacetimes [8][9][10] which were shown to constitute a rather broad and interesting subfamily of stationary axisymmetric fields. At the same time, the BM solution has also enlarged a class of metrics able to describe the interacting black holes -up to date the particular members of that class have been obtained and analyzed mainly in the context of the static vacuum [11][12][13], electrostatic [12,[14][15][16][17] or stationary vacuum [18][19][20] spacetimes with struts. While the paper [1] basically deals with the mathematical structure of the BM metric and associated equilibrium problem, it would certainly be of interest to better explore the physical properties of the spacetime whose subextreme sector provides excellent opportunities for the study of two interacting KN black holes and for extending the recent results on interacting Kerr sources [18] to the case of non-vanishing electromagnetic field.…”

On the simplest binary system of rotating black holes

“…In our paper [9] we explain how the desired expression for e(z) can be obtained with the aid of formula (2), and below we only give the final result involving three physical quantities, M, aandR:…”

“…The knowledge of (f permits one to reconstruct the entire metric, and the full set of corresponding metric functions determined by (4) can be found in [9].…”

Energy and Momentum Considerations in an Ideal Solenoid

“…The electromagnetic Poynting vector has long been of considerable interest over the years [1][2][3][4][5][6][7][8][9]. This is so because it is directly related to the electromagnetic (EM) energy flux and the electromagnetic linear momentum.…”