Some Properties of a New Solution of the Ernst Equation

TL;DR

This paper introduces a new three-parameter solution to the Ernst equation, linking it to Einstein's equations, and explores how the parameters affect the ergosphere's topology and the Penrose process.

Contribution

It presents a novel three-parameter solution to the Ernst equation with implications for the topology of the ergosphere and energy extraction processes.

Findings

The solution depends on three parameters related to mass and angular momentum.

A topological deformation of the ergosphere into a two-sheet surface is demonstrated.

Certain parameter values prevent the Penrose process.

Abstract

From a particularly simple solution of the Ernst equation, we build a solution of the vacuum stationary axisymmetric Einstein equations depending on three parameters. The parameters are associated to the total mass of the source and its angular momentum. The third parameter produces a topological deformation of the ergosphere making it a two-sheet surface, and for some of its values forbids the Penrose process.