Gauge and optical aspects of gravitation

Abstract

This is a rather personal review of a few fields of research in which the author has been involved and that he believes to be of relevance in the future. A brief description of the idea of gauge invariance and symmetry breaking is followed by a review of theories of the Kaluza-Klein type and of the Einstein-Cartan theory of gravitation with spin and torsion. It is shown that the early work of Bateman can be considered to provide a basis for an optical geometry in Lorentzian manifolds with shear-free congruences of null geodesics, a notion introduced by Robinson and closely connected to that of algebraically special gravitational fields. There is a natural, one-to-one correspondence between the set of such optical geometries and that of Cauchy-Riemann spaces. A few odd remarks are devoted to the problem of `large numbers', an EIH problem, variational principles and elementary links between gravitation and quantum physics.