Kerr-NUT-AdS metrics and string theory

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Title: Kerr-NUT-AdS metrics and string theory
Author: Chen, Wei
Abstract: 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 ?i that are subject to the constraint Ei ?2i = 1 . We find a coordinate reparameterisation in which the ?i variables are replaced by [D /2] ?1 unconstrained coordinates y ? , and put the coordinates r and y ? 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 .
URI: http : / /hdl .handle .net /1969 .1 /ETD -TAMU -2109
Date: 2009-05-15


Kerr-NUT-AdS metrics and string theory. Available electronically from http : / /hdl .handle .net /1969 .1 /ETD -TAMU -2109 .

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