## Generalised Robinson-Trautman and Kundt waves and their physical interpretation.

thesis

posted on 05.11.2013 by Peter Docherty#### thesis

In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.

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.

### History

#### School

- Science

#### Department

- Mathematical Sciences