Abstract:
In this thesis we consider several aspects of general relativity relating to
exact solutions of the Einstein equations. In the first part gravitational
plane waves in the Rosen form are investigated, and we develop a formalism
for writing down any arbitrary polarisation in this form. In addition to
this we have extended this algorithm to an arbitrary number of dimensions,
and have written down an explicit solution for a circularly polarized Rosen
wave. In the second part a particular, ultra-local limit along an arbitrary
timelike geodesic in any spacetime is constructed, in close analogy with the
well-known lightlike Penrose limit. This limit results in a Bianchi type I
spacetime. The properties of these spacetimes are examined in the context
of this limit, including the Einstein equations, stress-energy conservation and
Raychaudhuri equation. Furthermore the conditions for the Bianchi type I
spacetime to be diagonal are explicitly set forward, and the effect of the limit
on the matter content of a spacetime are examined.