A stationary q-metric

TL;DR

This paper introduces a stationary extension of the q-metric, an exact vacuum solution in Einstein's theory, incorporating parameters for mass, quadrupole moment, and angular momentum to model rotating, axially symmetric objects.

Contribution

It presents a new stationary q-metric solution that generalizes the static q-metric by including rotation and quadrupole parameters, expanding the modeling of compact objects.

Findings

The solution describes the exterior gravitational field of rotating, axially symmetric objects.

It relates the metric parameters to physical quantities like mass, quadrupole moment, and angular momentum.

The geometric and physical properties of the solution are thoroughly analyzed.

Abstract

We present a stationary generalization of the static $q-$metric, the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. It possesses three independent parameters that are related to the mass, quadrupole moment and angular momentum. We investigate the geometric and physical properties of this exact solution of Einstein's vacuum equations, and show that it can be used to describe the exterior gravitational field of rotating, axially symmetric, compact objects.