arXiv subjects
Publications and source records attributed to Alexandre M. Baranov.
The exact interior static solution of Einstein-Maxwell equations in Bondi's coordinates for the electrically charged fluid ball is obtained as a source of the Reissner-Nordström solution.
An approach to construction of static models is demonstrated for a fluid ball. Five examples are considered. Two of them are exact solutions of the Einstein equations; the other three are connected with the Airy special functions, the hypergeometric functions and the Heun functions.
Within the framework of General Relativity a model approach to a description of spherical gravitating static fluid balls with an electric charge is considered. The metric interval is written in Bondi's radiation coordinates. The total energy-momentum tensor as a direct sum of the perfect Pascal fluid energy-momentum tensor and the energy-momentum tensor of an electromagnetic field is chosen. The exact solution of the Einstein-Maxwell equations as an extension of similar solution with parabolic distribution of mass density is found.
We use the model approach to the description of spherical gravitating static fluid ball with an electric charge in general relativity. The metric is written in Bondi's coordinates. The total energy-momentum tensor (EMT) is chosen as a sum of the EMT of a Pascal perfect fluid and that of the electromagnetic field. An exact solution of the Einstein-Maxwell equations is found, extending a similar solution with parabolic mass density distribution.
A new exact static interior solution of the Einstein equations is obtained for a gravitating ball filled with a Pascal perfect fluid . The solution is an extension of the well-known interior solution with a parabolic distribution of mass density and describes more compact astrophysical objects such as neutron and hyperon stars. It is shown that a behaviour of the new mass density distribution near the stellar centre can be described as a cusp catastrophe.
A close relationship is demonstrated between the catastrophe theory, Petrov's algebraic classification of the gravitational fields and the theory of phase transitions.
A relativistic fluid ball with an inhomogeneous static stratified matter configuration is considered. A model of an astrophysical object with this structure of matter is constructed.
It is shown that at the center of gravitating fluid ball there is the phase transition of second kind of gravitational field as a change of field's algebraic type.
The exterior gravitational fields of the massive Schwarzschild, Kerr and NUT particles have an algebraic type {\bfseries D} according to Petrov's algebraic classification of the gravitational fields. A lightlike limit is input for these particles. It is shown that under this limiting procedure the gravitational fields of the particles are transformed into the gravitational fields of the lightlike particles a lighton and a helixon. On the other hand this limit can be described as a cusp catastrophe on a level of Weyl's matrix with a change of a gravitational field symmetry of such sources. In considered cases we have a phase gravitational transition of second kind from {\bfseries D} type into {\bfseries N} type or {\bfseries III} type. There is a transition of one "phase" to another. Petrov's algebraic types are the different "phases" of the gravitational field. It is shown that the lightlike sources in General Relativity "have no hairs".