arXiv subjects
Publications and source records attributed to B. V. Ivanov.
The stationary gravitational field of two identical counter-moving beams of pure radiation is found in full generality. The solution depends on an arbitrary function and a parameter which sets the scale of the energy density. Some of its properties are studied. Previous particular solutions are derived as subcases.
The gravitational field of a rigidly rotating cylinder of charged dust is found analytically. The general and all regular solutions are divided into three classes. The acceleration and the vorticity of the dust are given, as well as the conditions for the appearance of closed timelike curves.
The gravitational field of a rigidly rotating perfect fluid cylinder with gamma- law equation of state is found analytically. The solution has two parameters and is physically realistic for gamma in the interval (1.41,2]. Closed timelike curves always appear at large distances.
Interior perfect fluid solutions for the Reissner-Nordstrom metric are studied on the basis of a new classification scheme. General formulas are found in many cases. Explicit new global solutions are given as illustrations. Known solutions are briefly reviewed.
It is shown that for realistic anisotropic star models the surface redshift can not exceed the values 3.842 or 5.211 when the tangential pressure satisfies the strong or the dominant energy condition respectively. Both values are higher than 2, the bound in the perfect fluid case.
Interior perfect fluid solutions for the Reissner-Nordstrom metric are studied on the basis of a new classification scheme. It specifies which two of the fluid's characteristics are given functions and picks up accordingly one of the three main field equations, the other two being universal. General formulae are found for charged de Sitter solutions, the case of constant energy component of the energy-momentum tensor, the case of known pressure (including charged dust) and the case of linear equation of state. Explicit new global solutions, mainly in elementary functions, are given as illustrations. Known solutions are briefly reviewed and corrected.
It is shown that different approaches towards the solution of the Einstein equations for a static spherically symmetric perfect fluid with a gamma-law equation of state lead to an Abel differential equation of the second kind. Its only integrable cases at present are flat spacetime, de Sitter solution and its Buchdahl transform, Einstein static universe and the Klein-Tolman solution.
It is shown that almost all known solutions of the kind mentioned in the title are easily derived in a unified manner when a simple ansatz is imposed on the metric. The Whittaker solution is an exception, replaced by a new solution with the same equation of state.
The system of Einstein-Maxwell equations for fields mentioned in the title is simplified. Known pure radiation solutions are systematized and new solutions are given by separating the variables.
New expanding, axisymmetric pure-radiation solutions are found, exploiting the analogy with the Euler-Darboux equation for aligned colliding plane waves.
Pure-radiation solutions are found, exploiting the analogy with the Euler- Darboux equation for aligned colliding plane waves and the Euler-Tricomi equation in hydrodynamics of two-dimensional flow. They do not depend on one of the spacelike coordinates and comprise the Hauser solution as a special subcase.
An exact twisting type N vacuum solution is found. It has regular gauge and curvature invariants and decays to flat spacetime for big retarded times.
An exact solution is found describing the collision of axisymmetric pp-waves with M=0. They are impulsive in character and their coordinate singularities become point curvature singularities at the boundaries of the interaction region. The solution is conformally flat. Concrete examples are given, involving an ultrarelativistic black hole against a burst of pure radiation or two colliding beam- like waves.
A coordinate transformation is found which diagonalizes the axisymmetric pp-waves. Its effect upon concrete solutions, including impulsive and shock waves, is discussed.
It is shown that there are three vacuum and one electrovacuum solutions of diagonal plane waves with M=0 and constant Maxwell scalars. Namely, these are the single wave, Stoyanov, Babala and Bell-Szekeres solutions. A comparison is made with the planar solutions of Taub.