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Description:
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With the advent of supergravity and superstring theory , it is of great importance
to study higher -dimensional solutions to the Einstein equations . In this dissertation ,
we study the higher dimensional Kerr -AdS metrics , and show how they admit further
generalisations in which additional NUT -type parameters are introduced .
The choice of coordinates in four dimensions that leads to the natural inclusion
of a NUT parameter in the Kerr -AdS solution is rather well known . An important
feature of this coordinate system is that the radial variable and the latitude variable
are placed on a very symmetrical footing . The NUT generalisations of the highdimensional
Kerr -AdS metrics obtained in this dissertation work in a very similar way .
We first consider the Kerr -AdS metrics specialised to cohomogeneity 2 by appropriate
restrictions on their rotation parameters . A latitude coordinate is introduced in such
a way that it , and the radial variable , appeared in a very symmetrical way . The
inclusion of a NUT charge is a natural result of this parametrisation . This procedure
is then applied to the general D dimensional Kerr -AdS metrics with cohomogeneity
[D /2] . The metrics depend on the radial coordinate r and [D /2] latitude variables µi
that are subject to the constraint Ei µi² = 1 . We find a coordinate reparameterisation
in which the µi variables are replaced by [D /2] - 1 unconstrained coordinates yα , and
put the coordinates r and yα on a parallel footing in the metrics , leading to an
immediate introduction of ([D /2] - 1 ) NUT parameters . This gives the most general Kerr -NUT -AdS metrics in D dimensions .
We discuss some remarkable properties of the new Kerr -NUT -AdS metrics . We
show that the Hamilton -Jacobi and Klein -Gordon equations are separable in Kerr -
NUT -AdS metrics with cohomogeneity 2 . We also demonstrate that the general
cohomogeneity -n Kerr -NUT -AdS metrics can be written in multi -Kerr -Schild form .
Lastly , We study the BPS limits of the Kerr -NUT -AdS metrics . After Euclideanisation ,
we obtain new families of Einstein -Sassaki metrics in odd dimensions and
Ricci -flat metrics in even dimensions . We also discuss their applications in String
theory . |