Unequal binary configurations of interacting Kerr black holes

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 5parametric 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 Mi, angular momentum Ji, 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.

Thermodynamics of two aligned Kerr black holes

“…Sibgatullin's integral method [12] of constructing the exact solutions changed that unpleasant situation drastically, and thanks to it we now have at our disposal various analytical solutions for a pair of interacting Kerr black holes separated by a massless strut which are suitable for the study of the thermodynamic length in the stationary binary systems. Thus, in our paper we are going to consider the configurations of two equal counterrotating Kerr black holes [13,14], of two identical corotating Kerr black holes [15,16], and also the binary system composed of generic Kerr black holes [15,17,18]. We have decided to analyze the configurations of equal counter-and corotating black holes separately from the general case because the thermodynamical properties of these particular two-body systems were already discussed earlier in the literature [19,20], however, using exclusively the general formulas of the usual double-Kerr solution [9] restricted to the subextreme case only and not elaborating the explicit form of the particular cases; besides, the thermodynamic analysis of the corotating case in [20] is essentially based on numerical calculations.…”

Thermodynamics of Many Black Holes

“…The black holes are aligned along an axis, and are static in the sense of possessing a time-like Killing isometry in the region between the black hole and acceleration horizons. Though an Israel-Khan-like solution for two rotating black holes is known analytically [37,38], exact solutions for three or more Kerr black holes remain elusive 1 . To make the investigation of the system's thermodynamics accessible, we sidestep any discussion of rotation here.…”

Self-force on a static particle near a black hole

“…The described solution has been thoroughly analyzed in [48][49][50][51][52][53]. The most of physically interesting quantities has been calculated and we just list them here.…”