Showing papers on "Geodesic deviation published in 1990"

Periodic Trajectories for the Lorentz-Metric of a Static Gravitational Field

Abstract: In General Relativity a gravitational field is described by a symmetric, second order tensor $$ g \equiv g(z)\left[ {.,.} \right]z = ({z_0},...,{z_3})\varepsilon {^4} $$ on the space-time manifold R 4The tensor g is assumed to have the signature +, −, −, −; namely for all z ∈ R 4 the bilinear form g(z)[.,.] possesses one positive and three negative eigenvalues. The “pseudo-metric” induced by g is called Lorentz-metric.

Test particle motion around a magnetised Schwarzschild black hole

Abstract: Perturbations of equatorial geodesics of neutral test particles near a magnetised Schwarzschild black hole are studied by applying the equation of geodesic deviation and then numerically integrating the geodesic equation. Results of both approaches are compared and regions of stable circular orbits are determined. A precession of orbital planes inclined with respect to the equatorial plane and the effect of collimation of non-equatorial trajectories due to the external magnetic field are discussed. Null geodesics and orbits of electrically charged particles are studied in brief.

Paralleltransport and geodesic deviation in static spherically symmetric space-times

Abstract: Tetrads which are parallelpropagated along time-like geodesics in static spherically symmetric spce-times are constructed. Its connection with the geodesic precession is explained. Moreover, we express the solution of the equations of geodesic deviation in terms of the Killing vectors and the fourvelocity.

Geodesic deviation and Minikowski space

Abstract: We study the properties of the solution space of local surface-forming null “sub-congruences” in the neighbourhood of a given null geodesic in a pseudo-Riemannian space-time. This solution space is a three-dimensional manifold, naturally endowed with a conformai Minkowski metric.