A technique for generating new solutions of Einstein's equations

TL;DR

This paper introduces a straightforward method for generating new solutions to Einstein's equations by transforming functions that preserve the Ernst form, recovering known transformations and discovering a new asymptotically flat solution from Kerr.

Contribution

The paper develops a simple technique for solution generation in Einstein's equations, including the role of analytic transformations and a new solution derived from Kerr.

Findings

Recovered all known covariant Ernst transformations.

Identified the role of analytic transformations.

Derived a new asymptotically flat solution from Kerr.

Abstract

We present a simple technique for generating new solutions of Einstein's equations using such function transformations that leave the field equations in the Ernst form. In this context we recover all the known covariant transformations of Ernst equations and we find the role of the analytic ones. Finally we obtain a new asymptotically flat solution starting from the Kerr solutions.