New tools for determining the light travel time in static, spherically symmetric spacetimes beyond the order G2G^2

This paper is mainly devoted to the determination of the travel time of a photon as a function of the positions of the emitter and the receiver in a large class of static, spherically symmetric spacetimes. Such a function - often called time transfer function - is of crucial interest for testing metric theories of gravity in the solar system. Until very recently, this function was known only up to the second order in the Newtonian gravitational constant $G$ for a 3-parameter family of static, spherically symmetric metrics generalizing the Schwarzschild metric. We present here two procedures enabling to determine - at least in principle - the time transfer function at any order of approximation when the components of the metric are expressible in power series of the Schwarzschild radius of the central body divided by the radial coordinate. These procedures exclusively work for light rays which may be described as perturbations in power series in $G$ of a Minkowskian null geodesic passing through the positions of the emitter and the receiver. It is shown that the two methodologies lead to the same expression for the time transfer function up to the third order in $G$. The second procedure presents the advantage of exclusively needing elementary integrations which may be performed with any symbolic computer program whatever the order of approximation. The vector functions characterizing the direction of light propagation at the points of emission and reception are derived up to the third order in $G$. The relevance of the third order terms in the time transfer function is briefly discussed for some solar system experiments.Comment: 37 pages; published in "Frontiers in Relativistic Celestial Mechanics", vol. 2, ed. by S. M. Kopeikin, Series "De Gruyter Studies in Mathematical Physics 22", 2014. arXiv admin note: substantial text overlap with arXiv:1304.368

Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects

We present a complete analysis of the light rays within the linearized, weak-field approximation of a Schwarzschild-like metric describing the gravitational field of an isolated, spherically symmetric body. We prove in this context the existence of two time transfer functions and we obtain these functions in an exact closed-form. We are led to distinguish two regimes. In the first regime, the two time transfer functions correspond to rays which are confined in regions of spacetime where the weak-field approximation is valid. Such a regime occurs in gravitational lensing configurations with double images of a given source. We find the general expressions of the angular separation and the difference in light travel time between the two images. In the second regime, there exists only one time transfer function corresponding to a light ray remaining in a region of weak field. Performing a Taylor expansion of this function with respect to the gravitational constant, we obtain the Shapiro time delay completed by a series of so-called "enhanced terms". The enhanced terms beyond the third order are new.Comment: 12 pages, added one figure in section 3; a paragraph in Introduction rewritten without changing the argument; corrected typos; one reference added for section 2; Eq. (84) rewritten in a more elegant form; slightly revised argument in section 9, results unchange

The Early Upper Palaeolithic occupations of Willendorf II (Lower Austria): a contribution to the chronostratigraphic and cultural context of the beginning of the Upper Palaeolithic in Central Europe

International audienceWillendorf II is one of the rare sites to offer a good chronostratigraphic framework for the period between 45,000 and 25,000 B.P. in Central Europe. Located in the Wachau on a lower terrace of the Danube, it has yielded 9 archaeological layers classically ascribed to the early Upper Palaeolithic, the Aurignacian and the Gravettian. This paper deals with the chronostratigraphic and cultural background of the lowest layers 1-4 of the Willendorf sequence. With good 14C datings and chronostratigraphic observations, it is now possible to better document this key-period for the understanding of the appearance of Upper Palaeolithic industries in Central Europe

Les débuts de l'Aurignacien en Europe. Discussion à partir des sites de Geissenklösterle, Willendorf II, Krems-Hundssteig et Bacho Kiro

Résumé d'une thèse de doctorat soutenue en 2004 à l'université Paris X-Nanterre sous la direction de Jean-Michel GenesteInternational audienceDiscussion à partir des sites de Geissenklösterle, Willendorf II, Krems-Hundssteig et Bacho Kiro. Thèse soutenue le 9 février 2004 à l'université Paris X-Nanterre sous la direction de Jean-Michel Genest