Soliton solutions to the Einstein gravitational field equations in the presence of a spherically-symmetric static background field

Abstract

Using a differential geometry approach, we have found two sets of new solutions to Einstein's equation of gravity in the presence of a spherically-symmetrical gravitational background, like the Earth. The transverse and longitudinal components of the metric tensor representing the gravity waves are all soliton solutions, propagating towards the origin of the Earth. If we consider the situation where the static background field is absent, the solutions still remain soliton-like in nature. The difference between our result and Einstein's is attributed to the two approximations taken previously — weak field and ‘harmonic condition’.