Approximate gravitational field of a rotating deformed mass

TL;DR

This paper presents an approximate solution to Einstein's equations for a rotating, deformed mass, capturing small deviations from spherical symmetry and potentially differing from the Kerr solution.

Contribution

It introduces a new approximate solution using a power series expansion of the Ernst potential with parameters for quadrupole and angular momentum.

Findings

Describes deviations from spherical symmetry via perturbations.

Provides a potential alternative to the Kerr solution.

Captures multipole structure of rotating deformed masses.

Abstract

A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters representing the quadrupole and the angular momentum respectively. The main feature of the solution is a suitable description of small deviations from spherical symmetry through perturbations of the static configuration and the massive multipole structure by using those parameters. This quality of the solution might eventually provide relevant differences with respect to the description provided by the Kerr solution.