Model of the gravitational dipole

TL;DR

This paper introduces a gravitational dipole model analogous to a global monopole, analyzing its physical properties, validity, and the motion of test particles, revealing unique orbital behaviors influenced by the curved spacetime.

Contribution

It proposes a new gravitational dipole model, examines its properties, and studies test particle motion, highlighting effects on orbital trajectories compared to other cosmic structures.

Findings

The gravitational dipole creates a curved spacetime affecting test particle motion.

Orbits can form unfolding spirals or hyperbolas due to repulsive centrifugal forces.

In a special case, orbits are straight lines similar to a spinning cosmic string.

Abstract

A model of the gravitational dipole is proposed in a close analogy to that of the global monopole. The physical properties and the range of validity of the model are examined as is the motion of test particles in the dipole background. It is found that the metric of the gravitational dipole describes a curved space-time, so one would expect it to have a more pronounced effect on the motion of the test particles than the spinning cosmic string. It is indeed so and in the generic case the impact of repulsive centrifugal force results in a motion whose orbits when projected on the equatorial plane represent unfolding spirals or hyperbolas. Only in one special case these projections are straight lines, pretty much in a manner observed in the field of the spinning cosmic string. Even if open, the orbits are nevertheless bounded in the angular coordinate $\theta$.