Simple metric for a magnetized, spinning, deformed mass

Abstract

We present and discuss a 4-parameter stationary axisymmetric solution of the Einstein-Maxwell equations able to describe the exterior field of a rotating magnetized deformed mass. The solution arises as a system of two overlapping corotating magnetized non-equal black holes or hyperextreme disks and we write it in a concise explicit form very suitable for concrete astrophysical applications.An interesting peculiar feature of this solution is that its first four electric multipole moments are zeros; it also has a non-trivial extreme limit which we elaborate completely in terms of four polynomial factors. We speculate that the formation of the binary configurations of this type, which is accompanied by a drastic change of the system's total angular momentum due to strong dragging effects, might be one of the mechanisms giving birth to relativistic jets in the galactic nuclei.

Simplest static and stationary vacuum quadrupolar metrics

“…Then, taking into account that the total mass M and angular momentum J of the KC solution in the particular case (34) are defined by the formulas M = 2σ/p 0 and J = −M 2 q 0 /2, we can introduce j = −q 0 /2 and thus arrive at the axis expression of the solution (32) in which the values of the dimensionless angular momentum j are restricted by the inequality |j| < 1/2 since |q 0 | ≤ 1. Therefore, the extreme solution (32) of this section, and the solution (24) of [31] represent the analytically extended versions of the KC subcase (34). Mention, that the values |j| > 1/2 can be also covered by the KC solution, but only after a complex continuation of the parameters p → ip, σ → iσ, q 2 0 − p 2 0 = 1, so that |q 0 | ≥ 1.…”

“…In view of a not quite accurate statement made in the paper [31] concerning the relation of the extreme vacuum potential (24) of [31] to the well-known Kinnersley-Chitre (KC) 5parameter solution [32], we find it instructive to reexamine this issue in more detail. As we have been able to find out recently, the desired relation can be only established for nonzero values of the KC parameter β, which may look strange recalling that this parameter is responsible for counterrotation (see, e.g., [33]), while the solution (24) of [31], as well as the solution (32) of this paper, is equatorially symmetric. However, as we have discovered to our big surprise, under certain choices of other parameters in the KC solution, β can describe the corotating case too.…”

“…We also note that the extreme limit in the solution (21) occurs when d = 0 ⇔ q = − 1 4 −j 2 , and the form of the solution then can be worked out with the aid of the general formulas of Ref. [31]. In this case it is convenient to introduce the spheroidal coordinates x and y by the formulas…”

Equatorially symmetric configurations of two Kerr-Newman black holes

“…Due to its multipole structure (2) involving physically important multipole moments, the MMR metric is able to describe the exterior field of compact massive objects endowed with electric charge and magnetic dipole moment, and in this relation its most recent application was considered in the paper [4]. At the same time, the above formulas also contain, as special subfamilies, the solutions for two equal corotating KN sources, black holes or hyperextreme objects, and we now turn to the consideration of these binary configurations, mainly concentrating on the black-hole systems.…”

“…While the former application of that solution is better known in the literature (see, e.g., Refs. [3,4]), the latter possibility of solution's usage for the analysis of the black hole binary systems has been scantly exploited only recently in its pure vacuum sector, and therefore it would be certainly of interest to make use of the solution [1] (henceforth referred to as the MMR solution) for obtaining its physically interesting generic electrovacuum subfamilies representing two equal (up to the sign of the charges) Kerr-Newman (KN) black holes [5] separated by a massless strut [6]. The main objective of the present paper will be derivation and analysis of a nontrivial binary configuration of dyonic KN black holes carrying equal electric and opposite magnetic charges and formulation for it of the first law of thermodynamics.…”