The infinitesimal holonomy group structure of EEnstein-Maxwell space-times

Abstract

This paper further investigates and interprets the structure of Einstein-Maxwell space-times in terms of the infinitesimal holonomy groups (IHG) of theC ∞ Riemannian connection. In particular, this investigation provides a fundamental physical classification of Einstein-Maxwell space-times in terms of the IHG group structure of the Riemann curvature tensor. It will be shown that the Maxwell fieldsF μλ and *F μλ of a given Einstein-Maxwell space-time define a representation of a subalgebra of the Lie algebra of the IHG. The main results of this paper are stated in the form of two theorems and a corollary. Also the results obtained here indicate that physical insight could be gained by studying more general gauge fields in terms of the IHG of the relevant Einstein-Yang-Mills space-times.