256 research outputs found
Solutions of Higher Dimensional Gauss-Bonnet FRW Cosmology
We examine the effect on cosmological evolution of adding a Gauss-Bonnet term
to the standard Einstein-Hilbert action for a (1 + 3)+ d dimensional
Friedman-Robertson-Walker (FRW) metric. By assuming that the additional
dimensions compactify as a power law as the usual 3 spatial dimensions expand,
we solve the resulting dynamical equations and find that the solution may be of
either de Sitter or Kasner form depending upon whether the Gauss-Bonnet term or
the Einstein term dominates.Comment: 10 pages, references added/corrected, accepted for publication in
General Relativity and Gravitatio
Supergravity Black Holes and Billiards and Liouville integrable structure of dual Borel algebras
In this paper we show that the supergravity equations describing both cosmic
billiards and a large class of black-holes are, generically, both Liouville
integrable as a consequence of the same universal mechanism. This latter is
provided by the Liouville integrable Poissonian structure existing on the dual
Borel algebra B_N of the simple Lie algebra A_{N-1}. As a by product we derive
the explicit integration algorithm associated with all symmetric spaces U/H^{*}
relevant to the description of time-like and space-like p-branes. The most
important consequence of our approach is the explicit construction of a
complete set of conserved involutive hamiltonians h_{\alpha} that are
responsible for integrability and provide a new tool to classify flows and
orbits. We believe that these will prove a very important new tool in the
analysis of supergravity black holes and billiards.Comment: 48 pages, 7 figures, LaTex; V1: misprints corrected, two references
adde
Kovalevski exponents and integrability properties in class A homogeneous cosmological models
Qualitative approach to homogeneous anisotropic Bianchi class A models in
terms of dynamical systems reveals a hierarchy of invariant manifolds. By
calculating the Kovalevski Exponents according to Adler - van Moerbecke method
we discuss how algebraic integrability property is distributed in this class of
models. In particular we find that algebraic nonintegrability of vacuum Bianchi
VII_0 model is inherited by more general Bianchi VIII and Bianchi IX vacuum
types. Matter terms (cosmological constant, dust and radiation) in the Einstein
equations typically generate irrational or complex Kovalevski exponents in
class A homogeneous models thus introducing an element of nonintegrability even
though the respective vacuum models are integrable.Comment: arxiv version is already officia
Billiard Representation for Multidimensional Cosmology with Intersecting p-branes near the Singularity
Multidimensional model describing the cosmological evolution of n Einstein
spaces in the theory with l scalar fields and forms is considered. When
electro-magnetic composite p-brane ansatz is adopted, and certain restrictions
on the parameters of the model are imposed, the dynamics of the model near the
singularity is reduced to a billiard on the (N-1)-dimensional Lobachevsky
space, N = n+l. The geometrical criterion for the finiteness of the billiard
volume and its compactness is used. This criterion reduces the problem to the
problem of illumination of (N-2)-dimensional sphere by point-like sources. Some
examples with billiards of finite volume and hence oscillating behaviour near
the singularity are considered. Among them examples with square and triangle
2-dimensional billiards (e.g. that of the Bianchi-IX model) and a 4-dimensional
billiard in ``truncated'' D = 11 supergravity model (without the Chern-Simons
term) are considered. It is shown that the inclusion of the Chern-Simons term
destroys the confining of a billiard.Comment: 27 pages Latex, 3 figs., submit. to Class. Quantum Gra
Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back
We use numerical integrations to study the asymptotical behaviour of a
homogeneous but anisotropic Bianchi type IX model in General Relativity with a
massive scalar field. As it is well known, for a Brans-Dicke theory, the
asymptotical behaviour of the metric functions is ruled only by the Brans-Dicke
coupling constant with respect to the value -3/2. In this paper we examine if
such a condition still exists with a massive scalar field. We also show that,
contrary to what occurs for a massless scalar field, the singularity
oscillatory approach may exist in presence of a massive scalar field having a
positive energy density.Comment: 31 pages, 7 figures (low resolution
Cosmological dynamics of exponential gravity
We present a detailed investigation of the cosmological dynamics based on
gravity. We apply the dynamical system approach to both
the vacuum and matter cases and obtain exact solutions and their stability in
the finite and asymptotic regimes. The results show that cosmic histories exist
which admit a double de-Sitter phase which could be useful for describing the
early and the late-time accelerating universe.Comment: 17 pages LaTeX, 3 figure
O(d,d)-invariance in inhomogeneous string cosmologies with perfect fluid
In the first part of the present paper, we show that O(d,d)-invariance
usually known in a homogeneous cosmological background written in terms of
proper time can be extended to backgrounds depending on one or several
coordinates (which may be any space-like or time-like coordinate(s)). In all
cases, the presence of a perfect fluid is taken into account and the equivalent
duality transformation in Einstein frame is explicitly given. In the second
part, we present several concrete applications to some four-dimensional
metrics, including inhomogeneous ones, which illustrate the different duality
transformations discussed in the first part. Note that most of the dual
solutions given here do not seem to be known in the literature.Comment: 25 pages, no figures, Latex. Accepted for publication in General
Relativity and Gravitatio
A new experiment for the determination of the 18F(p,alpha) reaction rate at nova temperatures
The 18F(p,alpha) reaction was recognized as one of the most important for
gamma ray astronomy in novae as it governs the early 511 keV emission. However,
its rate remains largely uncertain at nova temperatures. A direct measurement
of the cross section over the full range of nova energies is impossible because
of its vanishing value at low energy and of the short 18F lifetime. Therefore,
in order to better constrain this reaction rate, we have performed an indirect
experiment taking advantage of the availability of a high purity and intense
radioactive 18F beam at the Louvain La Neuve RIB facility. We present here the
first results of the data analysis and discuss the consequences.Comment: Contribution to the Classical Novae Explosions conference, Sitges,
Spain, 20-24 May 2002, 5 pages, 3 figure
E10 and a "small tension expansion" of M Theory
A formal ``small tension'' expansion of D=11 supergravity near a spacelike
singularity is shown to be equivalent, at least up to 30th order in height, to
a null geodesic motion in the infinite dimensional coset space E10/K(E10) where
K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group
E10(R). For the proof we make use of a novel decomposition of E10 into
irreducible representations of its SL(10,R) subgroup. We explicitly show how to
identify the first four rungs of the E10 coset fields with the values of
geometric quantities constructed from D=11 supergravity fields and their
spatial gradients taken at some comoving spatial point.Comment: 4 page
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