Electrovacuum cylindrical stationary solutions in general relativity

TL;DR

This paper systematically studies stationary cylindrical solutions in Einstein-Maxwell theory, deriving exact solutions and classifying known and new cases, with a focus on the zero cosmological constant scenario.

Contribution

It provides a comprehensive classification and explicit integration of Einstein-Maxwell equations for stationary cylindrical spacetimes, including new solutions and connections to known cases.

Findings

Derived explicit solutions for stationary cylindrical spacetimes.

Identified subclasses corresponding to known solutions.

Classified solutions based on parameter restrictions.

Abstract

This paper presents a systematical study of stationary (rotating) cylindrical space-times of a Weyl form that are solutions to D=4 Einstein-Maxwell equations with cosmological constant. The corresponding equations of motion - with zero cosmological constant - are integrated. Then, several classes of exact solutions - obtained by restricting the range of the free constant parameters - are obtained and sub-cases corresponding to already known solutions are indicated.