From Schwarzschild to Kerr: Generating spinning Einstein-maxwell fields from static fields

TL;DR

This paper presents a method to generate spinning Einstein-Maxwell fields from static solutions using coordinate and invariance transformations, demonstrated by deriving rotating fields from static axisymmetric configurations.

Contribution

It introduces a unified transformation approach to produce spinning solutions from static ones in Einstein-Maxwell theory, extending the Kerr solution generation method.

Findings

Generated a family of rotating solutions with mass, angular momentum, and electromagnetic moments.

Demonstrated the method on Voorhees-Zipoy vacuum solutions.

Provided explicit examples of spinning Einstein-Maxwell fields.

Abstract

The Kerr solution is generated from the Schwarzschild solution by a simple combination of real global coordinate transformations and of invariance transformations acting on the space of stationary solutions of the Einstein-Maxwell equations. The same transformation can be used to generate a spinning field configuration from any static axisymmetric configuration. We illustrate this by generating from the continuous family of Voorhees--Zipoy vacuum solutions a family of solutions endowed with mass, angular momentum, dipole magnetic moment and quadrupole electric moment.