Stationary, charged Zipoy-Voorhees metric from colliding wave spacetime

TL;DR

This paper derives a stationary, charged Zipoy-Voorhees metric from colliding Einstein-Maxwell wave spacetimes using the Ernst formalism, linking dynamic interactions to static solutions with arbitrary topology.

Contribution

It introduces a method to transform colliding wave solutions into stationary, charged Zipoy-Voorhees metrics via local isometry, expanding the understanding of spacetime topologies.

Findings

Derived explicit expression for charged Zipoy-Voorhees metric

Established a transformation from colliding wave spacetimes to stationary solutions

Enhanced the understanding of spacetime topology in Einstein-Maxwell theory

Abstract

Through the Ernst formalism we provide expression for a class of colliding Einstein-Maxwell (EM) metrics with cross polarization. Local isometry is imposed as a means to transform interaction region of the spacetime into stationary, charged Zipoy-Voorhees (ZV) metric in Schwarzschild coordinates. The ZV-metric is known to describe planetary/stellar objects with arbitrary topology. "The world may be seen in a grain of sand" - William Blake.