Vladimir S. Manko

Double-Reissner-Nordström solution and the interaction force between two spherical charged masses in general relativity

The physical representation of the general double-Reissner-Nordstroem solution is obtained by rewriting the N=2 Breton-Manko-Aguilar electrostatic metric in the Varzugin-Chistyakov parametrization (M{sub i},Q{sub i},R). A concise analytical formula is derived for the interaction force between two arbitrary Reissner-Nordstroem constituents, and an example of the equilibrium configuration involving two oppositely charged particles which confirms earlier Bonnors prediction of the existence of such configurations is given.

Extended multi-soliton solutions of the Einstein field equations

Extended soliton solutions of the Einstein field equations obtained within the framework of Sibgatullins integral method are further analysed. We write the metric defining such solutions in a concise form suitable for concrete applications. The general formulae relating the parameters of the solution to the axis data and corresponding relativistic multipole moments are derived.

Exact solution of the double-Kerr equilibrium problem

We present concise analytic expressions for the Komar masses and angular momenta of the balancing Kerr-NUT constituents in the double-Kerr solution which complement the equilibrium formulae previously obtained (Manko V S, Ruiz E and Sanabria-Gomez J D 2000 Class. Quantum Grav. 17 3881). A rigorous proof of the non-existence of equilibrium states of two Kerr black holes with positive masses is given.

Extended multi-soliton solutions of the Einstein field equations: II. Two comments on the existence of equilibrium states

The results of our previous paper are applied to solving analytically the balance problem in the double-Kerr solution for all three possible types of binary systems, i.e. when a binary system is composed of two non-extreme black holes, of a non-extreme black hole and a hyperextreme object and of two hyperextreme objects. We also construct a new stationary electrovacuum metric representing binary systems of charged, magnetized, rotating, aligned masses involving one extreme object and on the basis of the numerical study of balance equations we conjecture that the equilibrium states in such systems are impossible.

ON THE EQUILIBRIUM OF CHARGED MASSES IN GENERAL RELATIVITY : THE ELECTROSTATIC CASE

The problem of the equilibrium of charged aligned masses is discussed within the framework of the electrostatic multi-soliton solution of the Einstein-Maxwell equations. The equilibrium states in a charged two-body system are considered in detail. We demonstrate the validity of Smarrs mass formula for a charged static black hole when the latter is in electrostatic equilibrium with a superextreme object.

A Kerr black hole in the external gravitational field

Abstract The full metric describing a Kerr black hole in an arbitrary static and axisymmetric gravitational field is presented in a concise analytical form which allows a straightforward verification of the mass formula for black holes. A sufficient condition of the regularity of the metric in the region exterior to the black hole horizon is formulated.

On the Physical Interpretation of δ= 2 Tomimatsu-Sato Solution

The physical properties of the Tomimatsu-Sato δ = 2 spacetime are analyzed, with emphasis on the issues of the negative mass distribution in this spacetime and the origin of a massless ring singularity. As a by-product of this analysis it is proved analytically that the Kerr spacetime with negative mass always has a massless naked ring singularity off the symmetry axis accompanied by a region with closed timelike curves. Subject Index: 420, 450

A remark on the mass–angular–momentum relation in the double-Kerr solution

A very simple relation between the coordinate distance, masses and angular momenta of two balancing Kerr particles is derived and compared with a recent approximate result published by Bonnor (2001 Class. Quantum Grav. 17 1381).

Equatorial symmetry/antisymmetry of stationary axisymmetric electrovac spacetimes

In this second paper devoted to the equatorial symmetry/antisymmetry of stationary axisymmetric electrovac spacetimes, we show how two theorems proved in our previous paper (Ernst et al 2006 Class. Quantum Grav. 23 4945) can be utilized to construct exact solutions that are equatorially symmetric or antisymmetric.

On a Simple Representation of the Kinnersley-Chitre Metric

A concise form of the Kinnersley-Chitre five-parameter metric for a spinning mass is obtained by exploiting a remarkable similarity between the metric’s factor structure and the analogous structure of the Tomimatsu-Sato solutions with even distortion parameter δ .T he corresponding general subfamily of asymptotically flat spacetimes containing four arbitrary real parameters is considered, and all configurations describing two extreme Kerr sources separated by a strut are identified and briefly discussed. Subject Index: 450, 451