Generalized black diholes

Abstract

A 5-parametric exact solution, describing a binary system composed of identical counter-rotating black holes endowed with opposite electromagnetic charges, is constructed. The addition of the angular momentum parameter to the static Emparan-Teo dihole model introduces magnetic charges into this two-body system. The solution can be considered as an extended model for describing generalized black diholes as dyons. We derive the explicit functional form of the horizon half-length parameter $\sigma$ as a function of the Komar parameters: Komar mass $M$, electric/magnetic charge $Q_{E }/ Q_{B}$, angular momentum $J$, and a coordinate distance $R$, where the parameters $(M, J, Q_E, Q_B, R)$ characterize the upper constituent of the system, while $(M, -J, -Q_E, -Q_B, R)$ are associated with the lower one. The addition of magnetic charges enhances the standard Smarr mass formula in order to take into account their contribution to the mass. The solution contains, as particular cases, two solutions already discussed in the literature.Comment: 8 pages, 3 figures, 1 table; accepted in Phys. Rev.

Comment on “Generalized black diholes”

“…Later, after learning about our results, Cabrera-Munguia et al [4] have published a similar representation of the 5-parameter EMR metric which only slightly differs from ours in the form of σ: their σ is obtainable from (1) via the substitution…”

“…Unfortunately, the issue of discrepancy between two σ's was not touched in the paper of Cabrera-Munguia et al, although logically this should have been the main subject of that paper. Moreover, the authors of [4] made reference to our article exclusively in the context of the 4-parameter solution, with no mention of our 5-parameter dyonic model. In the present comment we will show that the expression for σ obtained by Cabrera-Munguia el al.…”

“…First of all, we would like to remark that one might naively think that, since the 5-parameter solutions from [1,4] differ in the form of σ only, then the physically incorrect solution should not satisfy the field equations identically. However, this is not the case because in the solution construction procedure employed in the two papers the quantity σ is an arbitrary constant which may in principle be chosen in the infinite number of very exotic unphysical ways without violating the field equations.…”

Asymmetric black dyonic holes

“…Since monopolar terms, NUT sources [16], and total magnetic charge break the asymptotic flatness of the solution, one fixes the axis conditions to avoid them. The axis conditions are an algebraic system of equations given in [9,14]. To solve the algebraic equations for the axis conditions, one determines, from Eq.…”

“…In Einstein-Maxwell (EM) theory, a static axisymmetric dihole system exhibits an equatorial symmetry [6,7]. After introducing the rotation parameter the system turns out to become dyonic [8], therefore, duality properties are no longer fulfilled and the spacetime results to be invariant under an exchange between the electric and magnetic charges [9]. Moreover, if the black holes are counterrotating, with zero total angular momentum, the spacetime turns out to be equatorially antisymmetric [6].…”