Abstract:
In this thesis, we have investigated conformal symmetries of the Ricci tensor,
also known as conformal Ricci collineations (CRCs), for certain physically important
spacetimes including kantowski-Sachs spacetimes, static spacetimes
with maximal symmetric transverse spaces, non-static spherically symmetric
spacetimes and locally rotationally symmetric Bianchi type I and V spacetimes.
For each of these spacetimes, the CRC equations are solved in degenerate
as well as non-degenerate cases.
When the Ricci tensor is degenerate, it is observed that for all the above
mentioned spacetimes, the Lie algebra of CRCs is in nite-dimensional. For
non-degenerate Ricci tensor, it is shown that the spacetimes under consideration
always admit a nite-dimensional Lie algebra of CRCs.
For Kantowski-Sachs and locally rotationally symmetric Bianchi type V
metrics, we obtain 15-dimensional Lie algebras of CRCs, which is the maximum
dimension of conformal algebra for a spacetime. In case of static
spacetimes with maximal symmetric transverse spaces, the dimension of Lie
algebra of CRCs turned out to be 6, 7 or 15. Similarly, it is observed that
non-static spherically symmetric spacetimes may possess 5, 6 or 15 CRCs for
non-degenerate Ricci tensor. Finally, the dimension of Lie algebra of CRCs
for locally rotationally symmetric Bianchi type I spacetimes is shown to be
7- or 15-dimensional.
For all the above mentioned spacetimes, the CRCs are found subject
to some highly non-linear di erential constraints. In order to show that
the classes of CRCs are non-empty, some examples of exact form of the
corresponding metric satisfying these constraints are provided.
