Taistra Y. Modeling the propagation of electromagnetic waves in the Kerr space-time based on the analytical-geometric method

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

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  • 01.05.02 - Математичне моделювання та обчислювальні методи


Specialized Academic Board

Д 35.195.01

Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine


The work is devoted to modeling of influence of a gravitational field on an electromagnetic field in the general theory of relativity. A system of equations with respect to the 4-potential in the Newman-Penrose formalism is obtained and sufficient conditions for the decopuling of its equations in the general case and in the case of null field are established. In the Kerr space-time with Kinnersley gauge a general solution and a solution with separated variables in the form of one-way null fields was found. One-way null fields of arbitrary integer and half-integer spin values in a Petrov type space-time are considered, general solution and solution with separated variables of systems of equations in the Kerr space-time are found. The exact expressions of the components of the wave vector, phase and group velocities of the one-way null solution are found. The frequency dispersion of wave vector and the presence of an azimuthal angular momentum are revealed. It is established that in the Kerr space-time the wave vector is not null. The integral congruence of the wave vector is not geodesic. On the basis of a one-way null solution, a model of elliptically polarized radiation, emanating from the Kerr black hole, is constructed. The formula for the angle of rotation of the plane of polarization and the formulas of polarization angles are obtained. The model allows to study the propagation of electromagnetic waves in the entire frequency range and angle of inclination.


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