A case of non-minimal couplings between gravity and electromagnetic fields is presented. The field equations are worked out in the language of exterior differential forms. A class of exact charge screening solutions is given with a specific discussion on the polarisation and magnetisation of space-time. The consequences of non-minimal couplings to gravity are examined.

The gravitational field equations of Brans-Dicke theory are given in a 4-dimensional non-Riemannian space-time with torsion in the language of exterior differential forms. A class of pp-wave metrics together with the Brans-Dicke scalar field are used to derive the autoparallel equations of motion for non-spinning test masses. These are compared with the geodesic equations of motion and the differences are pointed out. The effects of the gradient of the Brans-Dicke scalar on the geodesic deviation equations in this non-Riemannian setting are also discussed.

The variational field equations of Brans-Dicke scalar-tensor theory of gravitation are given in a non-Riemannian setting in the language of exterior differential forms over 4-dimensional spacetimes. A conformally re-scaled Robinson-Trautman metric together with the Brans-Dicke scalar field are used to characterise algebraically special Robinson-Trautman spacetimes. All the relevant tensors are worked out in a complex null basis and given explicitly in an appendix for future reference. Some special families of solutions are also given and discussed.

A nonminimal coupling of Weyl curvatures to electromagnetic fields is considered in Brans-Dicke-Maxwell theory. The gravitational field equations are formulated in a Riemannian spacetime where the spacetime torsion is constrained to zero by the method of Lagrange multipliers in the language of exterior differential forms. The significance and ramifications of nonminimal couplings to gravity are examined in a pp-wave spacetime.

Sandwich gravitational waves are given globally in terms of step functions at the boundaries. Linearized Einstein-Weyl equations are solved exactly in this background in Rosen coordinates. Depending on the geometry and composition of the sandwich wave, the neutrino's energy-momentum redistributes itself. At the test field level, since the background will not change, the neutrino's energy density in particular will show variations between positive and negative extrema when crossing the sandwich wave. This may reveal facts about the weakly interacting neutrinos in cosmology.