Geodesics in a quasispherical 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.

arXiv comment30 pages latex

References in corpus (6)

• Geodesics in the Gamma spacetime
• Measuring multipole moments of Weyl metrics by means of gyroscopes
• On the active gravitational mass of a non-spherical source leaving hydrostatic equilibrium
• Relativistic Multipoles and the Advance of the Perihelia
• Non spherical sources of strong gravitational fields out of hydrostatic equilibrium
• Directional naked singularity in general relativity

Cited by in corpus (21)

• Accretion process onto super-spinning objects
• Harmonic oscillations of neutral particles in the $\gamma$-metric
• Geodesics of the hyperbolically symmetric black hole
• Generalized Kerr spacetime with an arbitrary mass quadrupole moment: geometric properties vs particle motion
• Axially symmetric static sources of gravitational field
• The Israel Theorem: What is Nature Trying to Tell Us?
• A source of a quasi--spherical space--time: The case for the M--Q solution
• Repulsive gravity near naked singularities and point massive particles
• Acceleration of particles to high energy via gravitational repulsion in the Schwarzschild field
• Geodesics in the linearized multipole solution: Distinguishing black holes from naked singularities
• From geodesics of the multipole solutions to the perturbed Kepler problem
• The Dynamical Behaviour of Test Particles in a Quasi-Spherical Spacetime and the Physical Meaning of Superenergy
• A general relativistic effect in quasi-spherical objects as the possible origin of relativistic jets
• Approximate gravitational field of a rotating deformed mass
• Linearized multipole solutions and their representation
• Source integrals of multipole moments for static space-times
• Event Horizon of the Monopole-Quadrupole solution: geometric and thermodynamic properties
• Connecting the exterior gravitational field with the energy momentum tensor of axially symmetric compact objects
• Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations
• Whom actually do multipole moments belong to?
• Geodesic dynamics in Chazy-Curzon spacetimes