Approximate Metric for a Rotating Deformed Mass

TL;DR

This paper introduces a simple, approximate Kerr-like metric with quadrupole moment, derived via perturbation, which can model rotating, slightly deformed astrophysical objects and match interior solutions.

Contribution

A new, simple Kerr-like metric with quadrupole moment is derived through perturbation, enabling better modeling of rotating deformed astrophysical objects.

Findings

The metric is as simple as the Kerr metric.

It can be matched to an interior solution.

It models objects with any Kerr rotation parameter and slight deformation.

Abstract

A new Kerr-like metric with quadrupole moment is obtained by means of perturbing the Kerr spacetime. The form of this new metric is simple as the Kerr metric. By comparison with the exterior Hartle-Thorne metric, it is shown that it could be matched to an interior solution. This approximate metric may represent the spacetime of a real astrophysical object with any Kerr rotation parameter a and slightly deformed.