Approximate Kerr-Newman-like Metric with Quadrupole

TL;DR

This paper develops an approximate Kerr-Newman-like metric incorporating quadrupole deformation, aiming to better model realistic astrophysical objects with charge, rotation, and slight deformation.

Contribution

It introduces a new approximate metric perturbing the Kerr-Newman solution to include quadrupole effects, enhancing realism for astrophysical modeling.

Findings

The metric includes mass-quadrupole and quadrupole-quadrupole terms.

It reduces to known post-linear quadrupole metrics when charge is zero.

The form remains simple and Kerr-Newman-like.

Abstract

The Kerr metric is known to present issues when trying to find an interior solution. In this work we continue in our efforts to construct a more realistic exterior metric for astrophysical objects. A new approximate metric representing the spacetime of a charged, rotating and slightly-deformed body is obtained by perturbing the Kerr-Newman metric to include the mass-quadrupole and quadrupole-quadrupole orders. It has a simple form, because is Kerr-Newman-like. Its post-linear form without charge coincides with post-linear quadrupole-quadrupole metrics already found.