An axially symmetric stationary N-center solution of Einstein's vacuum equations

TL;DR

This paper presents a new stationary vacuum solution to Einstein's equations for N rotating axially symmetric masses, generalizing static and non-distorted solutions like Zipoy and Kerr-NUT configurations.

Contribution

It introduces a novel solution method for Einstein's vacuum equations that describes multiple rotating and static axially symmetric masses simultaneously.

Findings

Derivation of a stationary N-center solution using the Euclidon method.

The solution encompasses static, rotating, and non-distorted cases.

Provides a unified framework for multiple axially symmetric mass configurations.

Abstract

Using the Euclidon method, a stationary solution of Einstein's vacuum equations was obtained, describing N rotating axially symmetric masses, which in the absence of rotation describes N arbitrary axially symmetric static masses, for example, N Zipoy masses on the axis of symmetry, and in the absence of distortion, N Kerr-NUT solutions.