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In this thesis, Newman-Penrose techniques are used to obtain some new exact solutions to Einstein's field equations of general relativity and to assist in the physical interpretation of some exact radiative space-times. Attention is restricted to algebraically special space-times with a twist-free, repeated principal null congruence. In particular, the Robinson-Trautman type N solutions, which describe expanding gravitational waves, are investigated for all possible values of the cosmological constant A and the Gaussian curvature parameter E. The wave surfaces are always (hemi-)spherical, with successive surfaces displaced along time-like, space-like or null lines, depending on E. Explicit sandwich waves of this class are studied in Minkowski, de Sitter or anti-de Sitter backgrounds and a particular family of such solutions, which can be used to represent snapping or decaying cosmic strings, is considered in detail. The singularity and global structure of the solutions is also presented. In the remaining part of the thesis, the complete family of space-times with a non-expanding, shear-free, twist-free, geodesic principal null congruence (Kundt waves), that are of algebraic type III and for which the cosmological constant (Ac) is non-zero, is presented. The possible presence of an aligned pure radiation field is also assumed. These space-times generalise the known vacuum solutions of type N with arbitrary Ac and type III with Ac = O. It is shown that there are two, one and three distinct classes of solutions when Ac is respectively zero, positive and negative and, in these cases, the wave surfaces are plane, spherical or hyperboloidal in Minkowski, de Sitter or anti-de Sitter backgrounds respectively. The singularities which occur in these space-times are interpreted in terms of envelopes of these wave surfaces. Again, by considering functions of the retarded time which "cross-over" between canonical types, sandwich waves are also studied. The limiting cases of these, giving rise to shock or impulsive waves, are also considered.

In this thesis we investigate Robinson-Trautman solutions of Einstein's gravity cou- pled to a matter field in higher dimensions, specifically a conformally invariant and non- linear electromagnetic field. The latter possesses in general a non-zero energy-momentum tensor, which provides a source term in Einstein's equations. We focus concretely on an electromagnetic field aligned with the null vector field generating the expanding con- gruence of Robinson-Trautman spacetimes. At the beginning, we review the concept of optical scalars for a null vector field in higher dimensions and we use those to define the higher-dimensional Robinson-Trautman class of spacetimes. Next, we solve the corre- sponding Einstein's equations and present the complete family of exact solutions of the theory under consideration. We then contrast the obtained results with the known ones for the linear Maxwell theory in higher dimensions. As a check, we also compare our results to the well-known results in D = 4, since in this case our matter theory reduces to the standard linear Maxwell theory. Finally, we study properties of a subfamily of solutions which represent the static black holes within our class. In particular, we ana- lyze the asymptotic behaviour, we show that a curvature singularity is always present for r → 0 and the...