The Bretón–Manko equatorially antisymmetric binary configuration revisited

Abstract

The Bretón-Manko solution for two identical counter-rotating Kerr-Newman charged masses is rewritten in the physical parametrization involving Komar quantities. The new form of the solution turns out to be very convenient for verifying that the black-hole sector of the Bretón-Manko binary configuration saturates a recent geometric inequality for interacting black holes with struts discovered by Gabach Clement.

Stationary black diholes

“…Though technically, Ref. [4] is correct, the solution itself, in our opinion, exhibits some unphysical features because of the presence in it of nonvanishing magnetic charges created by rotation of electric charges, which contradicts the known cases of a single KN solution and of the Bretón-Manko (BM) solution [6,7] for a pair of identical counterrotating KN black holes where the electric charges generate a dipole magnetic field without magnetic monopoles. As a consequence, the usual Smarr mass formula [8] (not taking into account the contribution of magnetic charges) does not hold for the black-hole constituents comprising that binary configuration, and, moreover, the expression of the important geometric quantity σ obtained in Ref.…”

“…As it is straightforward to elaborate by purely algebraic computing the explicit form of the Ernst potentials defined by the axis data (7), as well as the form of the corresponding metric functions f, γ, and ω entering the stationary axisymmetric line element below we will restrict ourselves to only writing out the final expressions which reproduce and generalize the analogous formulas of Ref. [4].…”

“…It has been recently shown [7] that the equally charged black-hole constituents of the BM configuration saturate the Gabach-Clement inequality for black holes with struts [12] which reads…”

Binary system of unequal counterrotating Kerr-Newman sources

“…Recently a more general description of such a problem is developed in Ref. [21], where the functional form of the horizon half-length parameter σ is introduced in terms of physical Komar parameters [22]. Furthermore, if the charges have opposite sign, the solution represents a counterrotating black dihole system [23,24], whose magnetic dipole moment is generated by the rotation of electrically charged black holes [25,26].…”

“…In fact, this paper deals with the unequal case of the solutions already discussed in Refs. [21,25], where now the seven physical parameters satisfy an algebraic relation which might be understood as a dynamic scenario between sources, since the physical properties of one body are affected by the presence of the other one. Later on, all the thermodynamical features of the system will be determined in a concise explicit form.…”