Generalized Kerr spacetime with an arbitrary mass quadrupole moment: geometric properties versus particle motion
An exact solution of Einstein's field equations in empty space first found in 1985 by Quevedo and Mashhoon is analyzed in detail. This solution generalizes Kerr spacetime to include the case of matter with an arbitrary mass quadrupole moment and is specified by three parameters, the mass M, the angular momentum per unit mass a and the quadrupole parameter q. It reduces to the Kerr spacetime in the limiting case q = 0 and to the Erez–Rosen spacetime when the specific angular momentum a vanishes. The geometrical properties of such a solution are investigated. Causality violations, directional singularities and repulsive effects occur in the region close to the source. Geodesic motion and accelerated motion are studied on the equatorial plane which, due to the reflection symmetry property of the solution, also turns out to be a geodesic plane.
Generalization of Kerr spacetime.
A class of exact solutions of the Einstein-Maxwell equations is presented. It represents the exterior gravitational field of a charged rotating mas. The class contains a generalization of the charged Kerr metric involving an infinite set of parameters that pertain to an axisymmetric deformation of the source
The Curzon singularity. II: Global picture
A new coordinate system is presented for the Curzon metric such that a class of incomplete geodesics are extendible both in the past and the future into regions of flat space. All other incomplete geodesics terminate at the (infinite curvature) singularity, which appears as a ring with finite radius and is naked. The Curzon solution emerges in this picture as a peculiar kind of sandwich wave. This and other physical interpretations such as a possible collapse scenario are discussed.