Deflection of light in time-periodic spherically symmetric gravitational fields

TL;DR

This paper derives formulas for light deflection in weak, time-periodic spherically symmetric gravitational fields, showing that in leading order, the deflection angle is unaffected by time oscillations.

Contribution

It introduces a perturbative method to calculate light deflection in time-periodic gravitational fields, extending static case formulas to dynamic scenarios.

Findings

Deflection angle formulas valid for both static and time-periodic metrics.

In leading order, the deflection angle is independent of time for oscillating scalar fields.

The approach applies to weak gravitational fields with spherical symmetry.

Abstract

Using the geodesic method and the perturbative approach, we study the deflection of light by time-periodic spherically symmetric gravitational fields. Assuming the weakness of the gravitational field, we derive general formulas that determine the deflection angle in the leading order approximation. The formulas are valid for both time-periodic and static metrics. Using these results, we calculate the deflection angle of a light ray passing through a spherically symmetric oscillating distribution of a self-gravitating scalar field with a logarithmic potential. It turned out that in this case the deflection angle does not depend on time in the leading order.