Approximate Kerr-like Metric with Quadrupole

TL;DR

This paper introduces a new approximate Kerr-like metric incorporating quadrupole deformation, useful for modeling rotating compact objects with improved accuracy and compatibility with existing solutions.

Contribution

It presents a simple, Kerr-like metric including second-order quadrupole effects, compatible with the Hartle-Thorne metric, enhancing modeling of rotating deformed bodies.

Findings

The metric matches second-order quadrupole metrics with slow rotation.

It can be transformed into an improved Hartle-Thorne metric.

The form is simple and suitable for studying compact objects.

Abstract

A new approximate metric representing the spacetime of a rotating deformed body is obtained by perturbing the Kerr metric to include til the second order of the quadrupole moment. It has a simple form, because is Kerr-like. Its Taylor expansion form coincides with second order quadrupole metrics with slow rotation already found. Moreover, it can be transformed to an improved Hartle-Thorne metric, this guarantees its validity to be useful in studying compact object, and that it is possible to find an inner solution.