Unequal binary configurations of interacting Kerr black holes

TL;DR

This paper derives an exact analytical solution describing the interaction of unequal Kerr black holes with a strut, providing formulas for horizons, forces, and thermodynamics based on physical parameters.

Contribution

It presents the first explicit 5-parameter asymptotically flat solution for unequal Kerr black hole interactions with detailed physical formulas.

Findings

Derived explicit formulas for black hole horizons and interaction forces.

Provided thermodynamical characteristics of each black hole in the system.

Analyzed limits and special cases of the solution.

Abstract

Stationary axisymmetric binary configurations of unequal Kerr sources with a massless strut among them are developed in a physical representation. In order to describe interacting black holes, the axis conditions in the most general case are solved analytically deriving the corresponding $5$-parametric asymptotically flat exact solution. In addition, we obtain concise formulas for the black hole horizons, the interaction force, as well as the thermodynamical characteristics of each source in terms of physical Komar parameters: mass $M_{i}$, angular momentum $J_{i}$, and coordinate distance $R$, where such parameters are contained inside of the coefficients of a cubic equation which can be interpreted as a dynamical law for interacting black holes with struts. Some limits are obtained and discussed.