Increase of the Number of Detectable Gravitational Waves Signals due to Gravitational Lensing

This article deals with the gravitational lensing (GL) of gravitational waves (GW). We compute the increase in the number of detected GW events due to GL. First, we check that geometrical optics is valid for the GW frequency range on which Earth-based detectors are sensitive, and that this is also partially true for what concerns the future space-based interferometer LISA. To infer this result, both the diffraction parameter and a cut-off frequency are computed. Then, the variation in the number of GW signals is estimated in the general case, and applied to some lens models: point mass lens and singular isothermal sphere (SIS profile). An estimation of the magnification factor has also been done for the softened isothermal sphere and for the King profile. The results appear to be strongly model-dependent, but in all cases the increase in the number of detected GW signals is negligible. The use of time delays among images is also investigated.Comment: Accepted for publication in General Relativity and Gravitatio

Gravitational perturbations on local experiments in a satellite : The dragging of inertial frame in the HYPER project

We consider a nearly free falling Earth satellite where atomic wave interferometers are tied to a telescope pointing towards a faraway star. They measure the acceleration and the rotation relatively to the local inertial frame. We calculate the rotation of the telescope due to the aberrations and the deflection of the light in the gravitational field of the Earth. We show that the deflection due to the quadrupolar momentum of the gravity is not negligible if one wants to observe the Lense-Thirring effect of the Earth. We consider some perturbation to the ideal device and we discuss the orders of magnitude of the phase shifts due to the residual tidal gravitational field in the satellite and we exhibit the terms which must be taken into account to calculate and interpret the full signal. Within the framework of a geometric model, we calculate the various periodic components of the signal which must be analyzed to detect the Lense-Tirring effect. We discuss the results which support a reasonable optimism. As a conclusion we put forward the necessity of a more complete, realistic and powerful model in order to obtain a final conclusion on the theoretical feasibility of the experiment as far as the observation of the Lense-Thirring effect is involved.Comment: Accepted in GRG (vol 36, Feb 2004

Quantum Tests of the Foundations of General Relativity

The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is capable of covering quantum phenomena too, will be proposed. It is shown that this generalised equivalence principle is valid for matter wave interferometry and for the dynamics of expectation values. In addition, the use of this equivalence principle makes it possible to determine the structure of the interaction of quantum systems with gravitational and inertial fields. It is also shown that the path of the mean value of the position operator in the case of gravitational interaction does fulfill this generalised equivalence principle.Comment: Classical and Quantum Gravity 15, 13 (1998

GRAVITATIONAL EXPERIMENTS WITH STABLE ELECTROMAGNETIC DEVICES

This article presents a general method for studying the effect of a gravitational field on the phases of an electromagnetic wave. The method employed covers a broad range of experiments within the limited framework of PPN theories to pick out orders of magnitude concerning the different kinds of experiments which may be performed on earth with astronomical sources of gravitation

Effects of the time delays in a non linear pendular Fabry-Perot

We study a one arm pendular Fabry-Perot interferometer with specifications corresponding to the two arms interferometers designed to detect gravitational radiation. We consider the non linearities originating from the radiation force and the effects of time delays due to the finite length of the arm. We derive the exact and the associated « predictivised » equations for the motion of the suspended mirror. We show that effects of time delays increase considerably the stability of the device when the optical relaxation time is of the order of the period of the pendulum, a case of relevance when light is recycled. However the thermal noise does not seem to be much modified when calculated within a simple approximation scheme

A preliminary discussion of Dulkyn interferometer

The Dulkyn interferometer in Kazan is an active ring laser where the light propagates along two different paths. It has been developed with the idea that it could detect low frequency gravitational waves on Earth. Considering Dulkyn as a detector of periodic strains of order of h ~ 10−22 at low frequencies (10−3 Hz−10−5 Hz) we calculate that 30 W is the order of magnitude of the optical power necessary to beat the photon noise in the case of a long observation time (T = 4 months) and a reasonable signal to noise ratio (r = 3). We estimate that the displacement noise of the mirrors must not exceed 5×10−19m/$\sqrt{{Hz}}$. Dulkyn is also sensitive to accelerations and rotations. The acceleration noise does not seem to be troublesome ($\widetilde{g}\lesssim 0.1{m} {s}^{-2}/\sqrt{{Hz}}$), but the angular velocity noise must be less than 5×10−11 s−1/$\sqrt{{Hz}}$. The maximum strain (10−22) is obtained with free (pendulous) mirrors. Out of resonance, the strain is many orders of magnitude smaller when the mirrors are fixed on a rigid support. Such a case would rule out the possibility of a detection. As a conclusion we emphasize that the Dulkyn design does not bring any decisive improvement for the detection of low frequency gravitational waves on Earth

Introduction to gravitational wave research

This is an introductory paper to theoretical and experimental gravitational wave research. In the first part, we give the precise mathematical description of a weak gravitational wave in the general framework of metric theories. Then we discuss the effect of these waves on material systems and the principle of the present detectors. The third part concerns the generation of gravitational radiations and reviews the possible astrophysical sources. Finally, we discuss the limitations and the state of the art of present detectors

Theoretical approaches to laser spectroscopy in the presence of gravitational fields

We present a general framework in which non-linear optical phenomena for an ensemble of accelerated atoms can be studied. We show the equivalence of various approaches through frame transformations. This equivalence is understood within the context of a covariant formalism which is briefly sketched. The choice of the frame, in which the atoms are not accelerated but where the light spectrum and the atomic source term are correspondingly modified, leads to the simplest calculation. It enables one to use the usual density matrix diagrams and associated rules. Explicit examples are given in the case of a sinusoidal gravitational wave. Finally a brief discussion of the signal-to-noise ratio of the sidebands induced by gravitational waves on saturation resonances is outlined.Nous présentons un cadre théorique général pour l'étude des processus d'optique non-linéaire relatifs à un ensemble d'atomes accélérés. Nous montrons l'équivalence de différentes approches grâce à des changements de système de référence. Cette équivalence est manifeste dans le cadre d'un formalisme covariant qui est brièvement exposé. Le choix du système de référence dans lequel les atomes ne sont pas accélérés, mais où le contenu spectral de la lumière et le terme de pompage atomique sont modifiés en conséquence, conduit aux calculs les plus simples. Ce choix permet l'utilisation des diagrammes de matrice densité habituels ainsi que des règles diagrammatiques associées. Des exemples sont explicitement calculés dans le cas d'une onde de gravitation sinusoidale. Finalement, on présente une brève discussion du rapport signal sur bruit des raies latérales induites par les ondes de gravitation sur les résonances de saturation