Metric of two balancing Kerr particles in physical parametrization

Abstract

The present paper aims at elaborating a completely physical representation for the general 4-parameter family of the extended double-Kerr spacetimes describing two spinning sources in gravitational equilibrium. This involved problem is solved in a concise analytical form by using the individual Komar masses and angular momenta as arbitrary parameters, and the simplest equatorially symmetric specialization of the general expressions obtained by us yields the physical representation for the well-known Dietz-Hoenselaers superextreme case of two balancing identical Kerr constituents. The existence of the physically meaningful "black hole-superextreme object" equilibrium configurations permitted by the general solution may be considered as a clear indication that the spin-spin repulsion force might actually be by far stronger than expected earlier, when only the balance between two superextreme Kerr sources was thought possible. We also present the explicit analytical formulas relating the equilibrium states in the double-Kerr and double-Reissner-Nordstr\"om configurations.Comment: 10 pages, 2 figures; references adde

Unequal binary configurations of interacting Kerr black holes

“…In the present paper we provide a 7-parametric asymptotically flat exact solution that permits the description * icabreramunguia@gmail.com of the most general case of a BS composed of two unequal Kerr-Newman (KN) BHs [7] separated by a massless strut, where the functional form of their BH horizons as well as all the thermodynamical properties contained in the Smarr formula [8] are given by concise formulae. Due to the fact that the conditions on the axis and the absence of individual magnetic charges are fulfilled, the full metric is completely characterized by physical Komar parameters: the masses M i , electric charges Q i , and angular momenta J i , while the centers of the sources are keeping apart by a coordinate distance R. In passing, we show that in a similar way as in the vacuum situation [1], the BHs interact via a dynamical law that is now defined by a septic algebraic equation, and when the strut is removed, it can be trivially reduced to some equilibrium laws already known; the case concerning vacuum systems [9] and the electrostatic one [10]. We also obtain quite trivial expressions for the thermodynamic relations of the BS during the merger limit (ML), whereas the result of Dietz and Hoenselaers [11] on the interaction force of two spinning particles at large distances has been generalized to include the contribution of the electric charges.…”

“…and Q 1 = 0 leads to the equilibrium law for vacuum systems [9]. The case concerning unequal counterrotating KN binary BHs [22] that is obtainable from Eqs.…”

“…We will refer to the last one research with the purpose to derive once again the final formulas for σ i obtainable from Eq. (25) in this equilibrium situation [11]…”

“…After that, we have been capable to obtain the nontrivial expressions for the BH horizons σ i , i = 1, 2, in terms of the five arbitrary physical Komar parameters {M 1 , M 2 , a 1 , a 2 , R} as well as the thermodynamical features included in the Smarr formula [31]. These five physical parameters are contained within the coefficients of a cubic equation which is interpreted as a dynamical law for interacting BHs, and it reduces to the equilibrium law for two arbitrary Kerr sources [11] in the absence of the strut. Another interesting physical property of the BS reveals that there exist equilibrium states without a strut during the MP on which the sources can be noticed as subextreme carrying both positive masses; this point is certainly intriguing an we hope to delve into it in greater depth in the future.…”

Metric for two arbitrary Kerr sources

“…Fortunately, the formulas of the present paper reveal that the above formula (14) still holds when the Kerr sources are hyperextreme. This conclusion is important for performing a correct transition to the case of equilibrium binary configurations without struts [17] when a = ±(R + M). Let us also mention that vanishing of F when m 1 (or m 2 ) is equal to zero means the reduction of the two-body metric to a single Kerr solution [18] independently of the value of a 1 (or a 2 ).…”