Ellipsoidal Spacetimes and the Kerr Metric

Definition

Ellipsoidal spacetimes: Metrics that determine the distance between two points in a coordinate system adapted for the description of ellipsoidal bodies.

Kerr metric: Solution of Einstein’s field equations that describes the exterior gravitational field of a rotating mass monopole.

Introduction

To this day, the best known theory that describes the gravitational interaction is Einstein’s theory (Misner et al., 2017). It states that a gravitational field is described by a spacetime with a metric which satisfies Einstein’s equations. It relates the geometry of spacetime, determined by the left-hand side of Einstein’s equations, with the energy-momentum distribution of matter which acts as the source of the gravitational field.

One of the main goals of relativistic geodesy is the complete description of the gravitational field of astrophysical compact objects, i.e., objects that are small for their mass. In general, the class of astrophysical compact objects is usually considered...