90 research outputs found
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
Tidal gravitational effects in a satellite
Atomic wave interferometers are tied to a telescope pointing towards a
faraway star in a nearly free falling satellite. Such a device is sensitive to
the acceleration and the rotation relatively to the local inertial frame and to
the tidal gravitational effects too. We calculate the rotation of the telescope
due to the aberration and the deflection of the light in the gravitational
field of a central mass (the Earth and Jupiter). Within the framework of a
general parametrized description of the problem, we discuss the contributions
which must be taken into account in order to observe the Lense-Thirring effect.
Using a geometrical model, we consider some perturbations to the idealized
device and we calculate the corresponding effect on the periodic components of
the signal. Some improvements in the knowledge of the gravitational field are
still necessary as well as an increase of the experimental capabilities;
however our conclusions support a reasonable optimism for the future. Finally
we put forward the necessity of a more complete, realistic and powerful model
in order to obtain a definitive conclusion on the feasibility of the experiment
as far as the observation of the Lense-Thirring effect is involved.Comment: accepted to General Relativity and Gravitatio
THE ''FORGOTTEN'' PROCESS : the emission stimulated by matter waves.
submitted in European Journal of PhysicsIn a famous paper where he introduces the A and B coefficients, Einstein considered that atomic decays of excited atoms can be stimulated by light waves. Here we consider that atomic decays can also be stimulated by atomic waves. It is however necessary to change the Maxwell-Boltzmann statistics of thermal equilibrium into Bose-Einstein statistics and to introduce a coefficient C which complements the list of the coefficients introduced by Einstein. Stimulated emission of light can be considered as the first step towards the laser. Similarly, stimulated production of matter waves can be considered as the basic phenomenon for an atom-laser. Most of the results that we obtain here are not new. However, the method that we use remains very close to elementary classical physics and emphasizes the symmetry between electromagnetic and matter waves from various points of view
A comparison between matter wave and light wave interferometers for the detection of gravitational waves
We calculate and compare the response of light wave interferometers and
matter wave interferometers to gravitational waves. We find that metric matter
wave interferometers will not challenge kilometric light wave interferometers
such as Virgo or LIGO, but could be a good candidate for the detection of very
low frequency gravitational waves
Optical response of a misaligned and suspended Fabry-Perot cavity
The response to a probe laser beam of a suspended, misaligned and detuned
optical cavity is examined. A five degree of freedom model of the fluctuations
of the longitudinal and transverse mirror coordinates is presented. Classical
and quantum mechanical effects of radiation pressure are studied with the help
of the optical stiffness coefficients and the signals provided by an FM
sideband technique and a quadrant detector, for generic values of the product
of the fluctuation frequency times the cavity round trip. A
simplified version is presented for the case of small misalignments. Mechanical
stability, mirror position entanglement and ponderomotive squeezing are
accommodated in this model. Numerical plots refer to cavities under test at the
so-called Pisa LF facility.Comment: 14 pages (4 figures) submitted to Phys. Rev.
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
Extended Fermi coordinates
We extend the notion of Fermi coordinates to a generalized definition in
which the highest orders are described by arbitrary functions. From this
definition rises a formalism that naturally gives coordinate transformation
formulae. Some examples are developped in which the extended Fermi coordinates
simplify the metric components.Comment: 16 pages, 1 figur
The Sagnac Effect in curved space-times from an analogy with the Aharonov-Bohm Effect
In the context of the natural splitting, the standard relative dynamics can
be expressed in terms of gravito-electromagnetic fields, which allow to
formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere
that this formal analogy can be used to derive the Sagnac effect in flat
space-time as a gravito-magnetic Aharonov-Bohm effect. Here, we generalize
those results to study the General Relativistic corrections to the Sagnac
effect in some stationary and axially symmetric geometries, such as the
space-time around a weakly gravitating and rotating source, Kerr space-time,
G\"{odel} universe and Schwarzschild space-time.Comment: 14 pages, 1 EPS figure, LaTeX, accepted for publication in General
Relativity and Gravitatio
The Sagnac Phase Shift suggested by the Aharonov-Bohm effect for relativistic matter beams
The phase shift due to the Sagnac Effect, for relativistic matter beams
counter-propagating in a rotating interferometer, is deduced on the bases of a
a formal analogy with the the Aharonov-Bohm effect. A procedure outlined by
Sakurai, in which non relativistic quantum mechanics and newtonian physics
appear together with some intrinsically relativistic elements, is generalized
to a fully relativistic context, using the Cattaneo's splitting technique. This
approach leads to an exact derivation, in a self-consistently relativistic way,
of the Sagnac effect. Sakurai's result is recovered in the first order
approximation.Comment: 18 pages, LaTeX, 2 EPS figures. To appear in General Relativity and
Gravitatio
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