Soliton Nature of Equilibrium State of Two Charged Masses in General Relativity

New derivation of static equilibrium state for two charged masses in General Relativity is given in the framework of the Inverse Scattering Method as an alternative to our previous derivation of this solution by the Integral Equation Method. This shows that such solution is of solitonic character and represents the particular case of more general (12-parametric) stationary axisymmetric electrovacuum two-soliton solution for two rotating charged objects obtained by one of the authors in 1986. This result gives an additional support to our comprehension that the appropriate analytical continuations of solitonic solutions in the space of their parameters are always possible and that applicability of the Inverse Scattering Method in presence of electromagnetic field is not restricted only to the cases with naked singularities.Comment: 7 pages, RevTeX

On the cosmological singularity

The long story of the oscillatory approach to the initial cosmological singularity and its more recent incarnation in multidimensional universe models is told.Comment: The invited paper for Proceedings of the XIII Marcel Grossmann Meeting (Stockholm, 2012) by reason of the Marcel Grossmann Award to V.A. Belinski and I.M. Khalatniko

On the integrable gravity coupled to fermions

In the present letter we indicate an extension of the pure gravity inverse scattering integration technique to the case when fermions (introduced on the base of supersymmetry) are present. In this way the integrability technique for simple ($N=1$) supergravity in two space-time dimensions coupled to the matter fields taking values in the Lie algebra of $E_{8\left( +8\right) }$ group is developed. This theory contains matter living only in one Weyl representation of $SO\left( 16\right)$ and represents the reduction to two dimensions of the three-dimensional simple supergravity constructed in [1]. Our spectral linear problem use superspace and covers the complete set of principal bosonic and fermionic equations of motion. This linear system, as in pure gravity, contains only the first order poles with respect to the spectral parameter. The procedure of constructing the exact super-solitonic solutions is outlined.Comment: Version 1611.02924v1 was withdrawn due to groundless assumption on the existence of the relation (43). In footnote 7 it was stressed that its proof remains to be seen. Analysis showed that such relation indeed is doubtful. Then the extension of the pure gravity inverse scattering method to superspace surely can cover only the simple integrable supergravity with E8(8) symmetr

Superposition of fields of two rotating charged masses in General Relativity and existence of equilibrium configurations

It is known that two Reissner-Nordstrom black holes or two overextreme Reissner-Nordstrom sources cannot be in physical equilibrium. In the static case such equilibrium is possible only if one of the sources is a black hole and another one is a naked singularity. We define the notion of physical equilibrium in general (stationary) case when both components of a binary system are rotating and show that such system containing a Kerr-Newman black hole and a Kerr-Newman naked singularity also can stay in physical equilibrium. The similar question about the system of two charged rotating black holes or two rotating overextreme charged sources still remains open.Comment: 20 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1211.396

Superposition of fields of two Reissner - Nordstrom sources

In this paper we present a 5-parametric family of static asymptotically flat solutions for the superposed gravitational and electromagnetic fields of two Reissner-Nordstr\"om sources with arbitrary parameters -- masses, charges and separating distance. A procedure for solving of the linear singular integral equation form of the electrovacuum Einstein - Maxwell equations for stationary axisymmetric fields is described in detail. The 4-parametric family of equilibrium configurations of two Reissner-Nordstr\"om sources (one of which should be a black hole and another one -- a naked singularity) presented in our recent paper \cite{Alekseev-Belinski:2007} arises after a restriction of the parameters of the 5-parametric solution presented here by the equilibrium condition which provides the absence in the solution of conical points on the symmetry axis between the sources.Comment: 24 pages, submitted to the Proceedings of the Eleventh Marcel Grossmann Meeting (Berlin, July 23 - 29, 2006

Complete integrability of higher-dimensional Einstein equations with additional symmetry, and rotating black holes

A new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution on a non-flat background is presented. It is intended to be an illustration of how the well-known Belinski-Zakharov method can be applied to find solutions of the Einstein equations in D-dimensional space-time with D-2 commuting Killing vectors using the complete integrability of this system. The method appears also to be promising for the analysis of the uniqueness questions for higher-dimensional black holes.Comment: 11 page

Mass ratio in SS433 revisited

We revisit the determination of binary mass ratio in the Galactic microquasar SS433 based on recent GRAVITY VLTI measurements of mass and angular momentum outflow through a circumbinary disc. The new observations combined with the constancy of the binary orbital period over $\sim 30$ yrs confirm that the mass ratio in SS433 is $q=M_\mathrm{x}/M_\mathrm{v}\gtrsim 0.6$. For the assumed optical star mass $M_\mathrm{v}$ ranging from $\sim 8$ to 15 $M_\odot$ such a mass ratio suggests a low limit of the compact object mass of $M_\mathrm{x}\sim 5-9 M_\odot$, placing the compact object in SS433 as a stellar-mass black hole.Comment: 4 pages, 3 figures, accepted in MNRAS, Main Journa