Analysis of nonmetric theories of gravity. I. Electromagnetism

In this article we are concerned with an analysis of nonmetric theories of gravity, and, in particular, with an analysis of a class of theories called metric-affine theories of gravity (MATG's). The purely gravitational laws of these theories are written down. We then establish a suitable set of laws representing electromagnetism in the presence of a gravitational field in metric-affine theories of gravity. We find that these laws simplify if we assume the gravitational field to be spherically symmetric and static. Consequently we define the concepts of spherical symmetry and staticity in the context of MATG's, and we calculate the form of the connection $\Gamma$ and the $\left(\left\{0\right\}\left\{2\right\}\right)$ tensor $g$ explicitly in such a gravitational field generated by a central mass. Finally, the laws that are established are investigated.