2,317 research outputs found
Non-topological gravitating defects in five-dimensional anti-de Sitter space
A class of five-dimensional warped solutions is presented. The geometry is
everywhere regular and tends to five-dimensional anti-de Sitter space for large
absolute values of the bulk coordinate. The physical features of the solutions
change depending on the value of an integer parameter. In particular, a set of
solutions describes generalized gravitating kinks where the scalar field
interpolates between two different minima of the potential. The other category
of solutions describes instead gravitating defects where the scalar profile is
always finite and reaches the same constant asymptote both for positive and
negative values of the bulk coordinate. In this sense the profiles are
non-topological. The physical features of the zero modes are discussed.Comment: 9 pages, 4 figure
Kink-antikink, trapping bags and five-dimensional Gauss-Bonnet gravity
Five-dimensional Gauss-Bonnet gravity, with one warped extra-dimension,
allows classes of solutions where two scalar fields combine either in a
kink-antikink system or in a trapping bag configuration. While the
kink-antikink system can be interpreted as a pair of gravitating domain walls
with opposite topological charges, the trapping bag solution consists of a
domain wall supplemented by a non-topological defect. In both classes of
solutions, for large absolute values of the bulk coordinate (i.e. far from the
core of the defects), the geometry is given by five-dimensional anti-de Sitter
space.Comment: 8 pages, 2 figure
Completitud y continuidad en Fundamentos de la geometrÃa de Hilbert: acerca del Vollständigkeitsaxiom (Completeness and Continuity in Hilbert’s Foundations of Geometry: on the Vollständigkeitsaxiom)
El artÃculo documenta y analiza las vicisitudes en torno a la incorporación de Hilbert de su famoso axioma de completitud, en el sistema axiomático para la geometrÃa euclÃdea. Esta tarea es emprendida sobre la base del material que aportan sus notas manuscritas para clases, correspondientes al perÃodo 1894–1905. Se argumenta que este análisis histórico y conceptual no sólo permite ganar claridad respecto de cómo Hilbert concibió originalmente la naturaleza y función del axioma de completitud en su versión geométrica, sino que además permite disipar equÃvocos en cuanto a la relación de este axioma con la propiedad metalógica de completitud de un sistema axiomático, tal como fue concebida por Hilbert en esta etapa inicial.
The paper reports and analyzes the vicissitudes around Hilbert’s inclusion of his famous axiom of completeness, into his axiomatic system for Euclidean geometry. This task is undertaken on the basis of his unpublished notes for lecture courses, corresponding to the period 1894–1905. It is argued that this historical and conceptual analysis not only sheds new light on how Hilbert conceived originally the nature of his geometrical axiom of completeness, but also it allows to clarify some misunderstandings regarding this axiom and the metalogical property of completeness of an axiomatic system, as it was understood by Hilbert in this initial stage
Time-dependent gravitating solitons in five dimensional warped space-times
Time-dependent soliton solutions are explicitly derived in a five-dimensional
theory endowed with one (warped) extra-dimension. Some of the obtained
geometries, everywhere well defined and technically regular, smoothly
interpolate between two five-dimensional anti-de Sitter space-times for fixed
value of the conformal time coordinate. Time dependent solutions containing
both topological and non-topological sectors are also obtained. Supplementary
degrees of freedom can be also included and, in this case, the resulting
multi-soliton solutions may describe time-dependent kink-antikink systems.Comment: 19 pages, 10 figure
Geometry, Formalism and Intuition: David Hilbert and the formal Axiomatic Method (1891-1905)
El artÃculo presenta y analiza un conjunto de notas manuscritas de clases para cursos sobre geometrÃa, dictados por David Hilbert entre 1891 y 1905. Se argumenta que en estos cursos el autor elabora la concepción de la geometrÃa que subyace a sus investigaciones axiomáticas en Fundamentos de la geometrÃa (1899). Por un lado, afirmo que lo que caracteriza esta concepción de la geometrÃa es: i) una posición axiomática abstracta o formal; ii) una posición empirista respecto del origen de la geometrÃa y de su lugar dentro de las distintas teorÃas matemáticas. Por otro lado, sostengo que el papel que Hilbert le confiere a la intuición geométrica en el proceso de axiomatización (formal) de esta teorÃa, permite apreciar claramente su oposición respecto de las posiciones formalistas (extremas) con las que habitualmente es identificado.The paper presents and analyzes a set of unpublished notes for lecture courses on geometry, which David Hilbert gave between 1891 and 1905. it will be argued that in these lecture courses the author elaborates the conception of geometry which underlies his axiomatic investigations in Foundations of Geometry (1899). on the one hand, it is claimed that this conception of geometry can be characterized by: i) an abstract or formal axiomatic view; ii) an empiricist stance regarding the origins of geometry and its place among the different mathematical theories. on the other hand, it is asserted that the role that Hilbert assigns to geometrical intuition in the process of the (formal) axiomatization of this theory, can be used to perceive his clear opposition with regard to (radical) formalist views which he is often identified with
Fluid phonons and inflaton quanta at the protoinflationary transition
Quantum and thermal fluctuations of an irrotational fluid are studied across
the transition regime connecting a protoinflationary phase of decelerated
expansion to an accelerated epoch driven by a single inflaton field. The
protoinflationary inhomogeneities are suppressed when the transition to the
slow roll phase occurs sharply over space-like hypersurfaces of constant energy
density. If the transition is delayed, the interaction of the quasi-normal
modes related, asymptotically, to fluid phonons and inflaton quanta leads to an
enhancement of curvature perturbations. It is shown that the dynamics of the
fluctuations across the protoinflationary boundaries is determined by the
monotonicity properties of the pump fields controlling the energy transfer
between the background geometry and the quasi-normal modes of the fluctuations.
After corroborating the analytical arguments with explicit numerical examples,
general lessons are drawn on the classification of the protoinflationary
transition.Comment: 30 pages, 3 figure
Heating up the cold bounce
Self-dual string cosmological models provide an effective example of bouncing
solutions where a phase of accelerated contraction smoothly evolves into an
epoch of decelerated Friedmann--Robertson--Walker expansion dominated by the
dilaton. While the transition to the expanding regime occurs at sub-Planckian
curvature scales, the Universe emerging after the bounce is cold, with sharply
growing gauge coupling. However, since massless gauge bosons (as well as other
massless fields) are super-adiabatically amplified, the energy density of the
maximally amplified modes re-entering the horizon after the bounce can
efficiently heat the Universe. As a consequence the gauge coupling reaches a
constant value, which can still be perturbative.Comment: 28 pages, 13 figure
Response of VIRGO detectors to pre-big-bang gravitons
The sensitivity achievable by a pair of VIRGO detectors to stochastic and
isotropic gravitational wave backgrounds produced in pre-big-bang models is
discussed in view of the development of a second VIRGO interferometer. We
describe a semi-analytical technique allowing to compute the signal-to-noise
ratio for (monotonic or non-monotonic) logarithmic energy spectra of relic
gravitons of arbitrary slope. We apply our results to the case of two
correlated and coaligned VIRGO detectors and we compute their achievable
sensitivities. We perform our calculations both for the usual case of minimal
string cosmological scenario and in the case of a non-minimal scenario where a
long dilaton dominated phase is present prior to the onset of the ordinary
radiation dominated phase. In this framework, we investigate possible
improvements of the achievable sensitivities by selective reduction of the
thermal contributions (pendulum and pendulum's internal modes) to the noise
power spectra of the detectors. Since a reduction of the shot noise does not
increase significantly the expected sensitivity of a VIRGO pair (in spite of
the relative spatial location of the two detectors) our findings support the
experimental efforts directed towards a substantial reduction of thermal noise.Comment: 23 pages in Latex styl
Inflation-Produced Magnetic Fields in R^n F^2 and I F^2 models
We re-analyze the production of seed magnetic fields during Inflation in
(R/m^2)^n F_{\mu \nu}F^{\mu \nu} and I F_{\mu \nu}F^{\mu \nu} models, where n
is a positive integer, R the Ricci scalar, m a mass parameter, and I \propto
\eta^\alpha a power-law function of the conformal time \eta, with \alpha a
positive real number. If m is the electron mass, the produced fields are
uninterestingly small for all n. Taking m as a free parameter we find that, for
n \geq 2, the produced magnetic fields can be sufficiently strong in order to
seed dynamo mechanism and then to explain galactic magnetism. For \alpha
\gtrsim 2, there is always a window in the parameters defining Inflation such
that the generated magnetic fields are astrophysically interesting. Moreover,
if Inflation is (almost) de Sitter and the produced fields almost
scale-invariant (\alpha \simeq 4), their intensity can be strong enough to
directly explain the presence of microgauss galactic magnetic fields.Comment: 5 pages, 2 figures. Minor revisions. References added. Accepted for
publication in Phys. Rev.
Gravitating multidefects from higher dimensions
Warped configurations admitting pairs of gravitating defects are analyzed.
After devising a general method for the construction of multidefects, specific
examples are presented in the case of higher-dimensional Einstein-Hilbert
gravity. The obtained profiles describe diverse physical situations such as
(topological) kink-antikink systems, pairs of non-topological solitons and
bound configurations of a kink and of a non-topological soliton. In all the
mentioned cases the geometry is always well behaved (all relevant curvature
invariants are regular) and tends to five-dimensional anti-de Sitter space-time
for large asymptotic values of the bulk coordinate. Particular classes of
solutions can be generalized to the framework where the gravity part of the
action includes, as a correction, the Euler-Gauss-Bonnet combination. After
scrutinizing the structure of the zero modes, the obtained results are compared
with conventional gravitating configurations containing a single topological
defect.Comment: 27 pages, 5 included figure
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