21 research outputs found

    Motion of a Vector Particle in a Curved Space-time. IV. Asymptotical shape of caustic

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    The studies of influence of spin on a photon motion in a Schwartzschild spacetime is continued. In the previous paper [2] the first order correction to the geodesic motion is reduced to a non-uniform linear ordinary differential equation and the equation obtained has been solved by the standard method of integration of the Green function. If each photon draws a world line specified by this solution then light rays from infinitely distant source form a caustic which does not appear without the spin-gravity interaction. The goal of the present work is to obtain explicit form of caustic.Comment: 6 page

    Electromagnetic field with constraints and Papapetrou equation

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    It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end the entire functional space of electromagnetic fields must be reduced to its subspace of locally plane monochromatic waves. We have formulated the constraints under which the entire functional space of electromagnetic fields reduces to its subspace of locally plane monochromatic waves. These constraints introduce variables of another kind which specify a field of local frames associated to the wave and contain some congruence of null-curves. The Lagrangian for constrained electromagnetic field contains variables of two kinds, namely, a congruence of null-curves and the field itself. This yields two kinds of Euler-Lagrange equations. Equations of first kind are trivial due to the constraints imposed. Variation of the curves yields the Papapetrou equations for a classical massless particle with helicity 1.Comment: 11 pages, PDF fil

    A stationary vacuum solution dual to the Kerr solution

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    We present a stationary axially symmetric two parameter vacuum solution which could be considered as ``dual'' to the Kerr solution. It is obtained by removing the mass parameter from the function of the radial coordinate and introducing a dimensionless parameter in the function of the angle coordinate in the metric functions. It turns out that it is in fact the massless limit of the Kerr - NUT solution.Comment: Latex, 4 pages, minor modifications in title and discussion. Accepted in Mod. Phys. Lett.

    The most general axially symmetric electrovac spacetime adimitting separable equations of motion

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    We obtain the most general solution of the Einstein electro - vacuum equation for the stationary axially symmetric spacetime in which the Hamilton-Jacobi and Klein - Gordon equations are separable. The most remarkable feature of the solution is its invariance under the duality transformation involving mass and NUT parameter, and the radial and angle coordinates. It is the general solution for a rotating (gravitational dyon) particle which is endowed with both gravoelectric and gravomagnetic charges, and there exists a duality transformation from one to the other. It also happens to be a transform of the Kerr - NUT solution. Like the Kerr family, it is also possible to make this solution radiating which asymptotically conforms to the Vaidya null radiation.Comment: 9 pages, RevTex, Accepted by Class. Quantum Grav. Title, Abstract and some expressions have been modified, typos corrected. The solution and main result remain unaltere

    Scalar and Spinor Perturbation to the Kerr-NUT Spacetime

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    We study the scalar and spinor perturbation, namely the Klein-Gordan and Dirac equations, in the Kerr-NUT space-time. The metric is invariant under the duality transformation involving the exchange of mass and NUT parameters on one hand and radial and angle coordinates on the other. We show that this invariance is also shared by the scalar and spinor perturbation equations. Further, by the duality transformation, one can go from the Kerr to the dual Kerr solution, and vice versa, and the same applies to the perturbation equations. In particular, it turns out that the potential barriers felt by the incoming scalar and spinor fields are higher for the dual Kerr than that for the Kerr. We also comment on existence of horizon and singularity.Comment: 31 pages including 20 figures, RevTeX style: Final version to appear in Classical and Quantum Gravit
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