Related papers: Soliton methods and the black hole balance problem
An intriguing open problem in general relativity is whether a stationary equilibrium configuration of multiple, physically relevant black holes can exist. In such a hypothetical setup, the gravitational attraction would need to be balanced…
The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are…
In this paper, we employ the general equatorially symmetric two-soliton solution of the Einstein-Maxwell equations for elaborating two physically meaningful configurations describing a pair of equal Kerr-Newman corotating black holes…
The inverse scattering method is applied to the investigation of the equilibrium configuration of black holes. A study of the boundary problem corresponding to this configuration shows that any axially symmetric, stationary solution of the…
A new method of construction of integral varieties of Einstein equations in three dimensional (3D) and 4D gravity is presented whereby, under corresponding redefinition of physical values with respect to anholonomic frames of reference with…
Based on the solution of a boundary problem for disconnected (Killing) horizons and the resulting violation of characteristic black hole properties, we present a non-existence proof for equilibrium configurations consisting of two aligned…
The Korteweg-de Vries and Benjamin-Ono nonlinear wave equations can describe solitary waves, all of which propagate in the same direction and which emerge from collisions with their shapes unchanged. There are technical challenges to giving…
In this work we intend to discuss the solitonic solutions of Einstein's field equations in vacuum by constructing the solution to N solitons and studying some aspects of it. In conclusion, it will be shown how the Kerr black hole can be…
We extend earlier discussions of the balance problem for two black holes and study stationary spacetimes containing an arbitrary number of $n$ aligned rotating and (possibly) charged black holes. For these hypothetical equilibrium…
Solitons and cavitons (localized solutions with singularities) for the nonlocal Whitham equations are studied. The equation of a fourth order with a parameter in front of fourth derivative for traveling waves is reduced to a reversible…
We study solitary wave solutions of the fifth-order Korteweg - de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear…
A brief review of recent research on soliton and black hole solutions of Einstein's equations with nonlinear field sources is presented and some open questions are pointed out.
The formation of spacetime singularities is a quite common phenomenon in General Relativity and it is regulated by specific theorems. It is widely believed that spacetime singularities do not exist in Nature, but that they represent a…
In Einstein-Maxwell theory, according to classic uniqueness theorems, the most general stationary black-hole solution is the axisymmetric Kerr-Newman metric, which is defined by three parameters: mass, spin and electric charge. The radial…
Analytical and numerical results on equilibrium configurations of rotating fluid bodies within Einstein's theory of gravitation are reviewed. Particular emphasis is placed on continuous parametric transitions to black holes. In this…
We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of $soliton$ $turbulence$ in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion…
Static, cylindrically symmetric solutions to nonlinear scalar-Einstein equations are considered. Regularity conditions on the symmetry axis and flat or string asymptotic conditions are formulated in order to select soliton-like solutions.…
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…
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…
Non-selfgravitating equilibrium tori orbiting around black holes have a long history and have been employed in numerous simulations of accretion flows onto black holes and other compact objects. We have revisited the problem of constructing…