Adding Twist to Anisotropic Fluids

TL;DR

This paper introduces a method to generate solutions for anisotropic fluids in spacetime that maintain certain symmetries, demonstrating its application with black string solutions and discussing potential uses.

Contribution

It presents a novel solution generating technique for anisotropic fluids that preserves specific Killing symmetries, expanding the toolkit for constructing such spacetimes.

Findings

Identified anisotropic matter distributions compatible with the Ehlers-Geroch transform

Applied the transformation to known spacetimes like the black string

Discussed potential applications of the method in generating new solutions

Abstract

We present a solution generating technique for anisotropic fluids which preserves specific Killing symmetries. Anisotropic matter distributions that can be used with the one parameter Ehlers-Geroch transform are discussed. Example spacetimes that support the appropriate anisotropic stress-energy are found and the transformation applied. The 3+1 black string solution is one of the spacetimes with the appropriate matter distribution. Use of the transform with a black string seed is discussed.