Passage of test particles through oscillating spherically-symmetric dark matter configurations

TL;DR

This paper develops a perturbative method to analyze the trajectories of test particles passing through oscillating dark matter distributions, deriving formulas for deflection angles applicable to both static and dynamic configurations.

Contribution

It introduces a general perturbative framework for calculating test particle trajectories in time-dependent spherically symmetric spacetimes caused by oscillating dark matter.

Findings

Deflection angles oscillate sinusoidally with amplitude.

Oscillations in deflection diminish for ultrarelativistic particles.

Formulas are valid for both static and dynamic matter distributions.

Abstract

Applying the perturbative approach to geodesic equations, we study motion of the test particles in time-dependent spherically symmetric spacetimes created by oscillating dark matter. Assuming the weakness of the gravitational field, we derive general formulas that describe infinite trajectories of the test particles and determine the total deflection angle in the leading order approximation. The obtained formulas are valid for both time-dependent and static matter configurations. Using these results, we calculate the deflection angle of a test particle passing through a spherically symmetric oscillating distribution of a self-gravitating scalar field with a logarithmic potential. It turned out that, in a wide range of amplitudes, oscillations in the deflection angle are sinusoidal and become small for ultrarelativistic particles.