On a New Formulation of Vacuum Axisymmetric Solutions of general Relativity

TL;DR

This paper introduces a novel formulation for vacuum axisymmetric solutions in general relativity, expressing solutions through functional dependencies on arbitrary functions, and provides specific examples illustrating this approach.

Contribution

It presents a new way to formulate vacuum axisymmetric solutions using functional dependencies, expanding the methods available for solving Einstein's equations.

Findings

Solutions depend on two pairs of functions, each based on an arbitrary single-variable function.

Examples demonstrate the applicability of the new formulation.

The approach simplifies the process of finding axisymmetric vacuum solutions.

Abstract

Axisymmetric Solutions of the vacuum Einstein equations are found in the Papapetrou-Weyl gauge. The solutions depend on two pairs of functionals, each pair of two functions depends on a different arbitrarily chosen function of one variable. Some examples are given.