Extreme binary black holes in a physical representation

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 M1 and M2, and a coordinate distance R, where the angular momenta J1 and J2 are functions of these parameters. Our physical representation allows us to identify some limits and novel physical properties.

Metric for two unequal extreme Kerr-Newman black holes

“…2 On the other hand, the vacuum solution earlier studied in Ref. [7] is the second trivial scenario that appears in the absence of electric charges Q 1 = Q 2 = 0, where after choosing ǫ = +1, Eq. ( 18) provides us a bicubic equation for co-rotating Kerr BHs that is given by…”

“…It contains nine parameters defined by the set {M, R, q, P 1 , P 2 , Q, B, q o , b o }. In the absence of electromagnetic field (Q and q o set to zero) the KCH exact solution [5,6] emerges straightforwardly after doing the simple redefinitions [7]…”

“…Similarly to the non-extreme case [14], the physical parameters are related to each other through an algebraic equation that represents a dynamical law for interacting BHs with struts. Unfortunately, there is no chance to solve exactly this higher degree equation except for some special unequal cases [7,16].…”

“…In static charged systems, the Majumdar-Papetrou metric [2][3][4] describes the simplest model of two extreme BHs, which remain in neutral equilibrium due to the balance of their electric charges and masses according to the relation Q i = ±M i , regardless of the separation distance among sources. Moreover, in vacuum systems, the Kinnersley-Chitre (KCH) exact solution [5] allows us the description of rotating binary BHs, after solving appositely the axis conditions [6,7]. In this type of binary vacuum systems, the Kerr BHs are apart by a conical singularity [8,9], which can give us information on their gravitational attraction and spin-spin interaction.…”

“…Hence, the Ernst potentials and metric functions will be depicted in terms of physical Komar parameters [15]: the masses M i , electric charges Q i , and a coordinate distance R as well. In this scheme, the five arbitrary parameters compose an algebraic equation thus defining a dynamical law for interacting BHs with struts, which is reduced to some previous studied cases [7,16]. At the same time, the metric is concisely given in terms of Perjes' factor structure [17].…”