Vladimir A. Belinski

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.

It is shown that inclusion of the shear stresses to the cosmological evolution can stabilize the Friedmann Big Bang. This results in the existence of the generic solution with isotropic 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.

This paper is a direct continuation of our old publication where it was found the exact solution of the Einstein-Maxwell equations for two static sources of Reissner-Nordstrom type in the state of the physical equilibrium. Here we present the exact solution of these equations for the case of two rotating charged sources and we proved the existence of the physical equilibrium state also for this general case.

It is shown here that there is no way for particle creation to occur by quantum tunneling through an infinitesimal neighborhood of the black hole horizon. This result is a trivial consequence of the regularity of the horizon, the equivalence principle and the general covariance of the relativistic theory of gravity. Moreover, we also confirm the less trivial statement that no particle creation by quantum tunneling through the black hole horizon is possible independent of the size of the presupposed tunneling domain.

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.

We demonstrate an alternative (with respect to the ones existing in literature) and more habitual for physicists derivation of exact solution of the Einstein-Maxwell equations for the motion of a charged spherical membrane with tangential tension. We stress that the physically acceptable range of parameters for which the static and stable state of the membrane producing the Reissner-Nordstrom (RN) repulsive gravity effect exists. The concrete realization of such state for the Nambu-Goto membrane is described. The point is that membrane are able to cut out the central naked singularity region and at the same time to join in appropriate way the RN repulsive region. As result we have a model of an everywhere-regular material source exhibiting a repulsive gravitational force in the vicinity of its surface: this construction gives a more sensible physical status to the RN solution in the naked singularity case.

The motion with intersections of relativistic gravitating shells in the Schwarzschild gravitational field of a central body is considered. Formulas are derived for calculating parameters of the shells after intersection via their parameters before intersection. Such special cases as the Newtonian approximation, intersections of light shells, and intersections of a test shell with a gravitating shell are also considered. The ejection of one of the shells to infinity in the relativistic region is described. The equations of motion for the shells are analyzed numerically.

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.