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 µ2i
= 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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2109 |
| Date | 15 May 2009 |
| Creators | Chen, Wei |
| Contributors | Pope, Christopher |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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