Remarks on Papapetrou Class of Vacuum Solutions of Einstein Equations

TL;DR

This paper explores a class of axially symmetric vacuum solutions to Einstein's equations, including the Papapetrou solution, and applies it to model the gravitational field of a line gravitomagnetic monopole.

Contribution

It derives a general solution for axially symmetric vacuum spacetimes and demonstrates its application to physical scenarios like a line gravitomagnetic monopole.

Findings

Derived a new class of solutions including Papapetrou as a special case

Showed the solution describes the external field of a mass with axial symmetry

Applied the solution to model spacetime around a line gravitomagnetic monopole

Abstract

Class of axially symmetric solutions of vacuum Einstein field equations including the Papapetrou solution as particular case has been found. It has been shown that the derived solution describes the external axial symmetric gravitational field of the source with nonvanishing mass. The general solution is obtained for this class of functions. As an example of physical application, the spacetime metric outside a line gravitomagnetic monopole has been obtained from Papapetrou solution of vacuum equations of gravitational field.