Motion of test particles in the field of a naked singularity

Understand

We investigate the motion of test particles in the gravitational field of a static naked singularity generated by a mass distribution with quadrupole moment.

• We use the quadrupole-metric ($q-$metric) which is the simplest generalization of the Schwarzschild metric with a quadrupole parameter.
• We study the influence of the quadrupole on the motion of massive test particles and photons and show that the behavior of the geodesics can drastically depend on the values of the quadrupole parameter.
• In particular, we prove explicitly that the perihelion distance depends on the value of the quadrupole.