21 research outputs found
Motion of a Vector Particle in a Curved Space-time. IV. Asymptotical shape of caustic
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
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
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
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
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