Abstract
The aim of this thesis is to study the projective
and curvature symmetries in nonstatic spacetimes. A study of
nonstatic spherically symmetric, nonstatic plane symmetric,
nonstatic cylindrically symmetric and special nonstatic axially
symmetric spacetimes according to their proper curvature
collineations (CCS) is given by using the rank of the 6× 6 Riemann
matrix and direct integration techniques. We consider the nonstatic
spherically symmetric spacetimes to investigate proper CCS. It has
been shown that when the above spacetimes admit proper CCS, they
turn out to be static spherically symmetric and form an infinite
dimensional vector space. In the nonstatic cases CCS are just
Killing vector fields. In case of nonstatic plane symmetric
spacetimes, it has been shown that when above spacetimes admit
proper CCS, they form an infinite dimensional vector space. We
consider the nonstatic cylindrically symmetric and special
nonstatic axially symmetric spacetimes to study the proper CCS. It
has been investigated that when above spacetimes admit proper CCS,
they also form an infinite dimensional vector space. We consider the
special nonstatic plane symmetric spacetimes to investigate proper
projective collineations. Following an approach developed by G.
Shabbir in [39], which basically consists of some algebraic and
direct integration techniques to study proper projective
collineations in the above spacetimes. It has been shown that when
the above spacetimes admit proper projective collineations, they
become a very special class of the spacelike or timelike versions of
FRW K=0 model.
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