2,583 research outputs found
A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge
In this paper, we study the recently discovered family of higher dimensional
Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse
metric is additively separable after multiplication by a simple function. This
allows us to separate the Hamilton-Jacobi equation, showing that geodesic
motion is integrable on this background. The separation of the Hamilton-Jacobi
equation is intimately linked to the existence of an irreducible Killing
tensor, which provides an extra constant of motion. We also demonstrate that
the Klein-Gordon equation for this background is separable.Comment: LaTeX, 14 pages. v2: Typo corrected and equation added. v3: Reference
added, introduction expanded, published versio
General Kerr-NUT-AdS Metrics in All Dimensions
The Kerr-AdS metric in dimension D has cohomogeneity [D/2]; the metric
components depend on the radial coordinate r and [D/2] latitude variables \mu_i
that are subject to the constraint \sum_i \mu_i^2=1. We find a coordinate
reparameterisation in which the \mu_i variables are replaced by [D/2]-1
unconstrained coordinates y_\alpha, and having the remarkable property that the
Kerr-AdS metric becomes diagonal in the coordinate differentials dy_\alpha. The
coordinates r and y_\alpha now appear in a very symmetrical way in the metric,
leading to an immediate generalisation in which we can introduce [D/2]-1 NUT
parameters. We find that (D-5)/2 are non-trivial in odd dimensions, whilst
(D-2)/2 are non-trivial in even dimensions. This gives the most general
Kerr-NUT-AdS metric in dimensions. We find that in all dimensions D\ge4
there exist discrete symmetries that involve inverting a rotation parameter
through the AdS radius. These symmetries imply that Kerr-NUT-AdS metrics with
over-rotating parameters are equivalent to under-rotating metrics. We also
consider the BPS limit of the Kerr-NUT-AdS metrics, and thereby obtain, in odd
dimensions and after Euclideanisation, new families of Einstein-Sasaki metrics.Comment: Latex, 24 pages, minor typos correcte
f(R) Theories of Supergravities and Pseudo-supergravities
We present f(R) theories of ten-dimensional supergravities, including the
fermionic sector up to the quadratic order in fermion fields. They are obtained
by performing the conformal scaling on the usual supergravities to the f(R)
frame in which the dilaton becomes an auxiliary field and can be integrated
out. The f(R) frame coincides with that of M-theory, D2-branes or NS-NS
5-branes. We study various BPS p-brane solutions and their near-horizon AdS
\times sphere geometries in the context of the f(R) theories. We find that new
solutions emerge with global structures that do not exist in the corresponding
solutions of the original supergravity description. In lower dimensions, We
construct the f(R) theory of N=2, D=5 gauged supergravity with a vector
multiplet, and that for the four-dimensional U(1)^4 gauged theory with three
vector fields set equal. We find that some previously-known BPS singular
"superstars" become wormholes in the f(R) theories. We also construct a large
class of f(R) (gauged) pseudo-supergravities. In addition we show that the
breathing mode in the Kaluza-Klein reduction of Gauss-Bonnet gravity on S^1 is
an auxiliary field and can be integrated out.Comment: Latex, 46 page
Electron spin relaxation in n-type InAs quantum wires
We investigate the electron spin relaxation of -type InAs quantum wires by
numerically solving the fully microscopic kinetic spin Bloch equations with the
relevant scattering explicitly included. We find that the quantum-wire size and
the growth direction influence the spin relaxation time by modulating the
spin-orbit coupling. Due to inter-subband scattering in connection with the
spin-orbit interaction, spin-relaxation in quantum wires can show different
characteristics from those in bulk or quantum wells and can be effectively
manipulated by various means.Comment: 8 pages, 6 figure
Separability in Cohomogeneity-2 Kerr-NUT-AdS Metrics
The remarkable and unexpected separability of the Hamilton-Jacobi and
Klein-Gordon equations in the background of a rotating four-dimensional black
hole played an important role in the construction of generalisations of the
Kerr metric, and in the uncovering of hidden symmetries associated with the
existence of Killing tensors. In this paper, we show that the Hamilton-Jacobi
and Klein-Gordon equations are separable in Kerr-AdS backgrounds in all
dimensions, if one specialises the rotation parameters so that the metrics have
cohomogeneity 2. Furthermore, we show that this property of separability
extends to the NUT generalisations of these cohomogeneity-2 black holes that we
obtained in a recent paper. In all these cases, we also construct the
associated irreducible rank-2 Killing tensor whose existence reflects the
hidden symmetry that leads to the separability. We also consider some
cohomogeneity-1 specialisations of the new Kerr-NUT-AdS metrics, showing how
they relate to previous results in the literature.Comment: Latex, 15 pages, minor typos correcte
Hole spin relaxation in semiconductor quantum dots
Hole spin relaxation time due to the hole-acoustic phonon scattering in GaAs
quantum dots confined in quantum wells along (001) and (111) directions is
studied after the exact diagonalization of Luttinger Hamiltonian. Different
effects such as strain, magnetic field, quantum dot diameter, quantum well
width and the temperature on the spin relaxation time are investigated
thoroughly. Many features which are quite different from the electron spin
relaxation in quantum dots and quantum wells are presented with the underlying
physics elaborated.Comment: 10 pages, 10 figure
Cosmological Solutions in String Theories
We obtain a large class of cosmological solutions in the
toroidally-compactified low energy limits of string theories in dimensions.
We consider solutions where a -dimensional subset of the spatial
coordinates, parameterising a flat space, a sphere, or an hyperboloid,
describes the spatial sections of the physically-observed universe. The
equations of motion reduce to Liouville or Toda equations, which
are exactly solvable. We study some of the cases in detail, and find that under
suitable conditions they can describe four-dimensional expanding universes. We
discuss also how the solutions in dimensions behave upon oxidation back to
the string theory or M-theory.Comment: Latex, 21 pages, a reference adjuste
Cosmological solutions, p-branes and the Wheeler-DeWitt equation
The low energy effective actions which arise from string theory or M-theory
are considered in the cosmological context, where the graviton, dilaton and
antisymmetric tensor field strengths depend only on time. We show that previous
results can be extended to include cosmological solutions that are related to
the E_N Toda equations. The solutions of the Wheeler-DeWitt equation in
minisuperspace are obtained for some of the simpler cosmological models by
introducing intertwining operators that generate canonical transformations
which map the theories into free theories. We study the cosmological properties
of these solutions, and also briefly discuss generalised Brans-Dicke models in
our framework. The cosmological models are closely related to p-brane solitons,
which we discuss in the context of the E_N Toda equations. We give the explicit
solutions for extremal multi-charge (D-3)-branes in the truncated system
described by the D_4 =O(4,4) Toda equations.Comment: 11 pages (2-column), Revte
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