Rotating magnetized black diholes

Abstract

We analyze a four-parameter class of asymptotically flat magnetized solutions to the Einstein-Maxwell equations constructed by Manko et al., and show that these represent systems of two co-rotating extreme black holes with equal masses and electric charges, and opposite magnetic and NUT charges, connected by a cosmic string. We discuss several three-parameter subclasses, and determine in each case the parameter domain in which the ring singularity is absent. We find a two-parameter subclass and a one-parameter subclass where the conical singularity is also absent in the horizon co-rotating frame. *

Balanced magnetized double black holes

“…We first review briefly the four-parameter family of magnetostatic solutions to the Einstein-Maxwell equations constructed in [8] and interpreted in [7] as the fields of double black hole systems. We recall that the Ernst potentials 1 E and ψ may be expressed in terms of Kinnersley potentials (U, V, W ) according to…”

“…In the parametrization of [7], the Kinnersley potentials of these solutions are given in prolate spheroidal coordinates by:…”

“…Both MP and IWP linear superpositions of two black holes with given physical characteristics (masses and charges) exist for an arbitrary separation between the two black holes. In a recent paper [7], we have investigated a class of four-parameter stationary asymptotically flat solutions to the Einstein-Maxwell equations previously constructed in [8], and shown that these represent non-linear superpositions of two rotating extreme black holes, their separation being intrincately related to the four black hole charges. Possible ring singularities can be avoided by an appropriate restriction of the parameter domain, though this was not addressed in the general case in [7].…”

“…In a recent paper [7], we have investigated a class of four-parameter stationary asymptotically flat solutions to the Einstein-Maxwell equations previously constructed in [8], and shown that these represent non-linear superpositions of two rotating extreme black holes, their separation being intrincately related to the four black hole charges. Possible ring singularities can be avoided by an appropriate restriction of the parameter domain, though this was not addressed in the general case in [7]. Interestingly, we found some one-and two-parameter subclasses in which the conical singularity is also absent in the horizon corotating frame, and pointed out that this does necessarily mean that the system is balanced.…”

“…In the next section, we briefly review the four-parameter class of solutions as presented in [7], and determine a necessary condition for the absence of ring singularity. In section 3 we find a two-parameter subclass of solutions with vanishing conical singularity, both in the horizon co-rotating frame and in the global frame (that of the observer at spacelike infinity).…”