A class of approximate exterior rotating solutions of Einstein's equations

Abstract

AbstractA class of approximate stationary vacuum solutions are obtained by expanding the metric in powers of a certain parameter, and by solving explicitly the first few orders in terms of two harmonic functions ø and ψ. These solutions, to the order considered, reduce to the Weyl solutions when ψ = 0 and yield the Papapetrou solutions when ø = 0, and contain a subclass that is asymptotically flat and has non-zero mass. The physical interpretation and the possibility of proceeding further are briefly discussed.