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 $1.4\times10^{-4}$. 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 $(3-4)\times 10^{-5}$ 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