A numerical study of approximate metrics with quadrupole moment

TL;DR

This paper investigates null geodesics in spacetimes characterized by mass, rotation, and a small quadrupole moment, analyzing how the quadrupole influences light scattering and spacetime deformation using symbolic-numeric methods.

Contribution

It introduces a numerical analysis of approximate metrics with quadrupole moments and visualizes their effects on null geodesics, expanding understanding of such spacetimes.

Findings

Quadrupole moment affects light scattering patterns.

Deformation of spacetime due to quadrupole is characterized.

Visualization of null geodesics in these metrics is achieved.

Abstract

Recently, spacetimes described by metrics with three parameters (mass, rotation and small quadrupole moment) was found, and in this paper, null geodesics for these metrics are calculated and visualized. Light scattering, as well as the role that the quadrupole moment plays in deforming these kinds of spacetimes are studied. This is a new application of a symbolic--numeric program that we previously used to study the Bonnor metric.