Cleaning Up a Tiny Part of the Exact Solution’s Augean Stable

Abstract

In the past century many exact solutions of Einstein’s field equations have been found and published. Some of these publications contain metrics which are not solutions of the Einstein field equations. This is due to typing errors in the one-forms or metrics, to the introduction of mysterious new coordinates after having carried out calculations in a different coordinate system or to the presentation of incorrect or incomplete solutions of some non-linear differential equations, etc. Also, many publications contain sets of supposedly different solutions to a given problem, which at a closer look can be seen to be special cases of others. As examples we look at the Newman Tamburino vacuum solutions and at the twisting type D solutions published by Frolov and Khlebnicov.