707 research outputs found
Contracting rigid germs in higher dimensions
Following Favre, we define a holomorphic germ f:(C^d,0) -> (C^d,0) to be
rigid if the union of the critical set of all iterates has simple normal
crossing singularities. We give a partial classification of contracting rigid
germs in arbitrary dimensions up to holomorphic conjugacy. Interestingly
enough, we find new resonance phenomena involving the differential of f and its
linear action on the fundamental group of the complement of the critical set.Comment: 30 pages, 0 figure
Sagnac Effect, Ring Lasers and Terrestrial Tests of Gravity
Light can be used as a probe to explore the structure of space-time: this is
usual in astrophysical and cosmological tests, however it has been recently
suggested that this can be done also in terrestrial laboratories. Namely, the
GINGER project aims at measuring post-Newtonian effects, such as the
gravito-magnetic ones, in an Earth based laboratory, by means of a ring lasers
array. Here, we first review the theoretical foundations of the Sagnac Effect,
on which ring lasers are based, and then we study the Sagnac Effect in a
terrestrial laboratory, emphasizing the origin of the gravitational
contributions that GINGER aims at measuring. Moreover, we show that accurate
measurements allow to set constraints on theories of gravity different from
General Relativity. Eventually, we describe the experimental setup of GINGER.Comment: 24 pages, 1 figure; accepted for publication in Galaxies, Special
Issue "Advances in Gravitational Research
Gravito-electromagnetic Aharonov-Bohm effect: some rotation effects revised
By means of the description of the standard relative dynamics in terms of
gravito-electromagnetic fields, in the context of natural splitting, we
formally introduce the gravito-magnetic Aharonov-Bohm effect. Then, we
interpret the Sagnac effect as a gravito-magnetic Aharonov-Bohm effect and we
exploit this formalism for studying the General Relativistic corrections to the
Sagnac effect in stationary and axially symmetric geometries.Comment: 19 pages, 2 figures, in in Proceedings of Analysis, Manifolds and
Geometric Structures in Physics, International Conference in Honour of Y.
Choquet-Bruhat, June 2004, Isola d'Elba, Ital
Gravitomagnetic Field of Rotating Rings
In the framework of the so-called gravitoelectromagnetic formalism, according
to which the equations of the gravitational field can be written in analogy
with classical electromagnetism, we study the gravitomagnetic field of a
rotating ring, orbiting around a central body. We calculate the gravitomagnetic
component of the field, both in the intermediate zone between the ring and the
central body, and far away from the ring and central body. We evaluate the
impact of the gravitomagnetic field on the motion of test particles and, as an
application, we study the possibility of using these results, together with the
Solar System ephemeris, to infer information on the spin of ring-like
structures.Comment: 8 pages, 2 figures; revised to match the version accepted for
publication in Astrophysics and Space Scienc
Gravito-electromagnetic Effects of Massive Rings
The Einstein field equations in linear post-Newtonian approximation can be
written in analogy with electromagnetism, in the so-called
gravito-electromagnetic formalism. We use this analogy to study the
gravitational field of a massive ring: in particular, we consider a continuous
mass distribution on Keplerian orbit around a central body, and we work out the
gravitational field generated by this mass distribution in the intermediate
zone between the central body and the ring, focusing on the gravito-magnetic
component that originates from the rotation of the ring. In doing so, we
generalize and complement some previous results that focused on the purely
Newtonian effects of the ring (thus neglecting its rotation) or that were
applied to the case of rotating spherical shells. Eventually, we study in some
simple cases the effect of the the rotation of the ring, and suggest that, in
principle, this approach could be used to infer information about the angular
momentum of the ring.Comment: 13 pages, LaTeX, revised to match the version accepted for
publication in the International Journal of Modern Physics
Light bending in gravity
In the framework of gravity, we focus on a weak-field and spherically
symmetric solution for the Lagrangian , where is
a small constant which parameterizes the departure from General Relativity. In
particular, we study the propagation of light and obtain the correction to the
general relativistic bending angle. Moreover, we discuss the impact of this
correction on some gravitational lensing observables, and evaluate the
possibility of constraining the theory parameter by means of
observations. In particular, on taking into account the astrometric accuracy in
the Solar System, we obtain that ; this bound is looser than those deriving from the analysis of
Solar System dynamics, e.g. ,
or . However we suggest that, since the effect only
depends on the impact parameter, better constraints could be obtained by
studying light bending from planetary objects.Comment: 14 pages, 1 figure; revised to match the version accepted for
publication in IJMP
Rotation Effects and The Gravito-Magnetic Approach
Gravito-electromagnetism is somewhat ubiquitous in relativity. In fact, there
are many situations where the effects of gravitation can be described by
formally introducing "gravito-electric" and "gravito-magnetic" fields, starting
from the corresponding potentials, in analogy with the electromagnetic theory
(see also A. Tartaglia's contribution to these proceedings). The "many faces of
gravito-electromagnetism" are related to rotation effects in both approximated
and full theory approaches. Here we show that, by using a 1+3 splitting,
relativistic dynamics can be described in terms of gravito-electromagnetic
(GEM) fields in full theory. On the basis of this formalism, we introduce a
"gravito-magnetic Aharonov-Bohm effect", which allows to interpret some
rotation effects as gravito-magnetic effects. Finally, we suggest a way for
measuring the angular momentum of celestial bodies by studying the
gravito-magnetic effects on the propagation of electromagnetic signals.Comment: 3 pages, LaTeX, 1 EPS figure; to appear in the Proceedings for the
``XVI SIGRAV Conference'' in Vietri sul Mare (SA) 13-16 September 2004,
References Changed, Misprints Correcte
A reversible allelic partition process and Pitman sampling formula
We introduce a continuous-time Markov chain describing dynamic allelic
partitions which extends the branching process construction of the Pitman
sampling formula in Pitman (2006) and the birth-and-death process with
immigration studied in Karlin and McGregor (1967), in turn related to the
celebrated Ewens sampling formula. A biological basis for the scheme is
provided in terms of a population of individuals grouped into families, that
evolves according to a sequence of births, deaths and immigrations. We
investigate the asymptotic behaviour of the chain and show that, as opposed to
the birth-and-death process with immigration, this construction maintains in
the temporal limit the mutual dependence among the multiplicities. When the
death rate exceeds the birth rate, the system is shown to have reversible
distribution identified as a mixture of Pitman sampling formulae, with negative
binomial mixing distribution on the population size. The population therefore
converges to a stationary random configuration, characterised by a finite
number of families and individuals.Comment: 17 pages, to appear in ALEA , Latin American Journal of Probability
and Mathematical Statistic
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