Geodesics in a Quash-Spherical Spacetime: A Case of Gravitational Repulsion

Abstract

Geodesics are studied in one of the Weyl metrics, referred to as the M-Q solution. First, arguments are provided, supporting our belief that this space-time is the more suitable (among the known solutions of the Weyl family) for discussing the properties of strong quasi-spherical gravitational fields. Then, the behaviour of geodesics is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry. Particular attention deserves the change of sign in proper radial acceleration of test particles moving radially along symmetry axis, close to the r = 2M surface, and related to the quadrupole moment of the source.2

A general relativistic effect in quasi-spherical objects as the possible origin of relativistic jets

“…In a recent study on the motion of test particles in the M-Q spacetime [4], it was shown that particles moving along radial geodesics experience an attractive force, as one expects, except when they move along the symmetry axis. In this latter case a repulsive force measured by a locally Minkowskian observer -regarded as a positive radial proper acceleration measured by this observer -appears close to the horizon if q < 0 (which corresponds to an oblate source) and even if it is arbitrarily small (though different from zero).…”

“…In this letter we want to call the attention to a possible explanation to at least some of these jets, which is based on the sign change of radial proper acceleration of test particles along the symmetry axis, close to the horizon of compact objects, and related to the quadrupole moment of the source [4] (although strictly speaking the term "horizon" refers to the spherically symmetric case, we shall use it when considering the r = 2M surface, in the case of small deviations from sphericity).…”

Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

“…For these metrics some properties of geodesic motion have been analyzed [22,23]. Geodesics in the Erez-Rosen spacetime have been also extensively investigated [24,25].…”

A source of a quasi-spherical space–time: The case for the M–Q solution

“…An study of the geodesics in this spacetime, has been recently presented [24] In the next section we shall construct a source for M-Q (1) solution.…”