Abstract
Stationary axisymmetric binary systems of unequal co and counter-rotating extreme Kerr black holes apart by a conical singularity are studied. Both solutions are well identified as two $3$-parametric subfamilies of the Kinnersley-Chitre metric, and fully depicted by Komar parameters: the two masses $M_{1}$ and $M_{2}$, and a coordinate distance $R$, where the angular momenta $J_{1}$ and $J_{2}$ are functions of these parameters. Our physical representation allows us to identify some limits and novel physical properties.
Highlights
The well-known Kinnersley-Chitre (KCH) 5-parametric exact solution [1] represents the extreme limit case of the so-called double-Kerr-NUT solution developed by Kramer and Neugebauer in 1980 [2], which allows to treat the superposition of two massive rotating sources in General Relativity
A few years ago, after following the ideas provided by Yamazaki [3] to eliminate the NUT parameter, Manko and Ruiz [6] solved for the first time in analytical way the axis condition that disconnects the region in between sources, with the main purpose to describe co and counter-rotating binary black hole (BH) systems separated by a conical singularity [7, 8]; i.e, a massless strut related with the interaction force among sources which is a measure of their gravitational attraction as well as the spin-spin interaction
II we describe the KCH exact solution as well as the two approaches considered earlier in Refs. [3, 6]; in particular, the path used by Manko and Ruiz to solve the axis conditions in order to describe interacting binary BHs by means of two 3-parametric special members of the KCH metric
Summary
The well-known Kinnersley-Chitre (KCH) 5-parametric exact solution [1] represents the extreme limit case of the so-called double-Kerr-NUT solution developed by Kramer and Neugebauer in 1980 [2], which allows to treat the superposition of two massive rotating sources in General Relativity. Both solutions permits us to study the dynamical interaction among two Kerr-type sources in stationary axisymmetric spacetimes by solving properly the corresponding axis conditions.
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