Stationary double black hole without naked ring singularity

Abstract

Recently double black hole vacuum and electrovacuum metrics attracted attention as exact solutions suitable for visualization of ultra-compact objects beyond the Kerr paradigm. However, many of the proposed systems are plagued with ring curvature singularities. Here we present a new simple solution of this type which is asymptotically Kerr, has zero electric and magnetic charges, but is endowed with magnetic dipole moment and electric quadrupole moment. It is manifestly free of ring singularities, and contains only a mild string-like singularity on the axis corresponding to a distributional energymomentum tensor. Its main constituents are two extreme co-rotating black holes carrying equal electric and opposite magnetic and NUT charges.

Rotating magnetized black diholes

“…This string can be removed by applying an external magnetic field, at the expense of asymptotic flatness. Recently, we have shown [9] that a rotating solution to the Einstein-Maxwell equations previously constructed in [10] represents a more complex system of two extreme black holes with equal masses and electric charges, and opposite magnetic and gravimagnetic (NUT) charges, co-rotating at an angular velocity fine-tuned to one-fourth of the inverse NUT charge. A third, necessary partner in this system is an electrically charged, magnetized strut or string which also acts as a Dirac-Misner string.…”

“…Both the Bonnor solution and the solution studied in [9] belong to a larger four-parameter class of solutions constructed with the aid of Sibgatullin's method [11] by Manko et al in [12], where their connection with neutron star models was suggested. Perhaps because of their complexity, the properties of these solutions have not, to our knowledge, been investigated.…”

On the Smarr formulas for electrovac spacetimes with line singularities

“…At the same time, the magnetic term was shown not to enter into the Smarr formula for the horizon mass 1 . In fact, in more general situations with several disconnected black holes joined by struts and Misner and Dirac strings, typical for various double black hole solutions, the same kind of calculations proved to be successful [33,34,35].…”

“…Although the corresponding distributional stress-energy tensor does not have such a simple physical interpretation, mathematically it belongs to the same class. Double black holes [33,34,34,35] carrying magnetic and NUT charges may contain struts, ensuring their equilibrium, with the properties of cosmic strings with positive or negative conical defect angles, as well as Dirac and Misner string carrying distributional magnetic and gravimagnetic fields, respectively. We will be not interested in the detailed structure of the distributional sources, but we would like to determine the masses, angular momenta, and electric charges generated by them.…”

“…The physical domain (bulk) will thus be bounded by these cylinders and a two-dimensional sphere at infinity Σ ∞ . Typical examples are solutions with NUTs including single and binary black holes [33,34,35].…”