The gravimagnetic dipole

TL;DR

This paper analyzes a stationary vacuum solution describing two black holes with NUT charges connected by a tensioned string, revealing force behaviors, unique tensionless configurations, and implications for black hole uniqueness and mechanics.

Contribution

It introduces a new exact solution for two black holes with NUT charges connected by a Misner string, exploring force interactions and tensionless configurations.

Findings

Large separation force can be attractive or repulsive.

Small separation force is always repulsive.

Existence of a tensionless Misner string configuration.

Abstract

We investigate a previously constructed stationary solution of the vacuum Einstein equations, which represents a system of two non-extreme black holes with equal masses and opposite NUT charges, connected by a Misner string with tension. For large separations, the inverse square law force measured by this tension is attractive or repulsive, according to the relative values of the masses and NUT charges. For small separations, the force is always repulsive, so that the system cannot collapse to a single black hole. For given values of the black hole masses and NUT charges, there is a unique configuration such that the Misner string is tensionless. This behaves asymptotically as the Kerr solution, but can be overspinning while remaining free from a ring singularity, thus evading the usual black hole uniqueness theorems. All double black hole and string configurations satisfy a generalized first law of black hole mechanics where the two black holes and the Misner string are treated on an equal footing.