2,340 research outputs found
On Hopf's Lemma and the Strong Maximum Principle
In this paper we consider Hopf's Lemma and the Strong Maximum Principle for
supersolutions to a class of non elliptic equations. In particular we prove a
sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum
Principle and we give a condition which is at once necessary for the validity
of Hopf's Lemma and sufficient for the validity of the Strong Maximum
Principle.Comment: 27 pages,4 figure
Relativistic formulation of coordinate light time, Doppler and astrometric observables up to the second post-Minkowskian order
Given the extreme accuracy of modern space science, a precise relativistic
modeling of observations is required. In particular, it is important to
describe properly light propagation through the Solar System. For two decades,
several modeling efforts based on the solution of the null geodesic equations
have been proposed but they are mainly valid only for the first order
Post-Newtonian approximation. However, with the increasing precision of ongoing
space missions as Gaia, GAME, BepiColombo, JUNO or JUICE, we know that some
corrections up to the second order have to be taken into account for future
experiments. We present a procedure to compute the relativistic coordinate time
delay, Doppler and astrometric observables avoiding the integration of the null
geodesic equation. This is possible using the Time Transfer Function formalism,
a powerful tool providing key quantities such as the time of flight of a light
signal between two point-events and the tangent vector to its null-geodesic.
Indeed we show how to compute the Time Transfer Functions and their derivatives
(and thus range, Doppler and astrometric observables) up to the second
post-Minkowskian order. We express these quantities as quadratures of some
functions that depend only on the metric and its derivatives evaluated along a
Minkowskian straight line. This method is particularly well adapted for
numerical estimations. As an illustration, we provide explicit expressions in
static and spherically symmetric space-time up to second post-Minkowskian
order. Then we give the order of magnitude of these corrections for the
range/Doppler on the BepiColombo mission and for astrometry in a GAME-like
observation.Comment: 22 pages, 5 figures, accepted in Phys. Rev.
Frequency shift up to the 2-PM approximation
A lot of fundamental tests of gravitational theories rely on highly precise
measurements of the travel time and/or the frequency shift of electromagnetic
signals propagating through the gravitational field of the Solar System. In
practically all of the previous studies, the explicit expressions of such
travel times and frequency shifts as predicted by various metric theories of
gravity are derived from an integration of the null geodesic differential
equations. However, the solution of the geodesic equations requires heavy
calculations when one has to take into account the presence of mass multipoles
in the gravitational field or the tidal effects due to the planetary motions,
and the calculations become quite complicated in the post-post-Minkowskian
approximation. This difficult task can be avoided using the time transfer
function's formalism. We present here our last advances in the formulation of
the one-way frequency shift using this formalism up to the
post-post-Minkowskian approximation.Comment: 4 pages, submitted to proceedings of SF2
UB CCD photometry of the old, metal rich, open clusters NGC 6791, NGC 6819 and NGC 7142
We report on a UV-oriented imaging survey in the fields of the old,
metal-rich open clusters, NGC 6791, NGC 6819 and NGC 7142. These three clusters
represent both very near and ideal stellar aggregates to match the distinctive
properties of the evolved stellar populations, as in elliptical galaxies and
bulges of spirals. The CMD of the three clusters is analyzed in detail, with
special emphasis to the hot stellar component. We report, in this regard, one
new extreme horizontal-branch star candidate in NGC 6791. For NGC 6819 and
7142, the stellar luminosity function points to a looser radial distribution of
faint lower Main Sequence stars, either as a consequence of cluster dynamical
interaction with the Galaxy or as an effect of an increasing fraction of binary
stars toward the cluster core, as actually observed in NGC 6791 too.Comment: 12 pages with 15 Figures & 5 Tables. To appear in the Astronomical
Journa
Light propagation in the field of a moving axisymmetric body: theory and application to JUNO
Given the extreme accuracy of modern space science, a precise relativistic
modeling of observations is required. We use the Time Transfer Functions
formalism to study light propagation in the field of uniformly moving
axisymmetric bodies, which extends the field of application of previous works.
We first present a space-time metric adapted to describe the geometry of an
ensemble of uniformly moving bodies. Then, we show that the expression of the
Time Transfer Functions in the field of a uniformly moving body can be easily
derived from its well-known expression in a stationary field by using a change
of variables. We also give a general expression of the Time Transfer Function
in the case of an ensemble of arbitrarily moving point masses. This result is
given in the form of an integral easily computable numerically. We also provide
the derivatives of the Time Transfer Function in this case, which are mandatory
to compute Doppler and astrometric observables. We particularize our results in
the case of moving axisymmetric bodies. Finally, we apply our results to study
the different relativistic contributions to the range and Doppler tracking for
the JUNO mission in the Jovian system.Comment: 17 pages, 4 figures, submitted to Phys. Rev. D, some corrections
after revie
A critical appraisal of ATLAS9 and NextGen 5 model atmospheres
The fitting atmosphere parameters (Teff, g, and [Fe/H]) for over 300 stars in
the Gunn & Striker and Jacoby et al. catalogs have been obtained relying on the
Kurucz (1992) ATLAS9 and Hauschildt et al (1999) NextGen5 synthesis models. The
output results are compared, and a critical appraisal of both theoretical codes
is performed.Comment: 2 pages, 2 figures; proceedings of "New Quests in Stellar
Astrophysics: The link between Stars and Cosmology", 26-30 March, 2001,
Puerto Vallarta, Mexico, eds. M. Chavez, A. Bressan, A. Buzzoni & D. Mayya,
to be published by the Kluwer Academic Publisher
Test of the gravitational redshift with stable clocks in eccentric orbits: application to Galileo satellites 5 and 6
The Einstein Equivalence Principle (EEP) is one of the foundations of the
theory of General Relativity and several alternative theories of gravitation
predict violations of the EEP. Experimental constraints on this fundamental
principle of nature are therefore of paramount importance. The EEP can be split
in three sub-principles: the Universality of Free Fall (UFF), the Local Lorentz
Invariance (LLI) and the Local Position Invariance (LPI). In this paper we
propose to use stable clocks in eccentric orbits to perform a test of the
gravitational redshift, a consequence of the LPI. The best test to date was
performed with the Gravity Probe A (GP-A) experiment in 1976 with an
uncertainty of . Our proposal considers the opportunity of
using Galileo satellites 5 and 6 to improve on the GP-A test uncertainty. We
show that considering realistic noise and systematic effects, and thanks to a
highly eccentric orbit, it is possible to improve on the GP-A limit to an
uncertainty around after one year of integration of
Galileo 5 and 6 data.Comment: 13 pages, 5 figures, accepted in Classical and Quantum Gravity as a
Fast Track Communicatio
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