36 research outputs found
Operational significance of the deviation equation in relativistic geodesy
Deviation equation: Second order differential equation for the 4-vector which
measures the distance between reference points on neighboring world lines in
spacetime manifolds.
Relativistic geodesy: Science representing the Earth (or any planet),
including the measurement of its gravitational field, in a four-dimensional
curved spacetime using differential-geometric methods in the framework of
Einstein's theory of gravitation (General Relativity).Comment: 9 pages, 4 figures, contribution to the "Encyclopedia of Geodesy".
arXiv admin note: text overlap with arXiv:1811.1047
A Snapshot of J. L. Synge
A brief description is given of the life and influence on relativity theory
of Professor J. L. Synge accompanied by some technical examples to illustrate
his style of work
Gravitational Waves Astronomy: a cornerstone for gravitational theories
Realizing a gravitational wave (GW) astronomy in next years is a great
challenge for the scientific community. By giving a significant amount of new
information, GWs will be a cornerstone for a better understanding of
gravitational physics. In this paper we re-discuss that the GW astronomy will
permit to solve a captivating issue of gravitation. In fact, it will be the
definitive test for Einstein's general relativity (GR), or, alternatively, a
strong endorsement for extended theories of gravity (ETG).Comment: To appear in Proceedings of the Workshop "Cosmology, the Quantum
Vacuum and Zeta Functions" for the celebration of Emilio Elizalde's sixtieth
birthday, Barcelona, March 8-10, 201
Gravito-electromagnetic analogies
We reexamine and further develop different gravito-electromagnetic (GEM)
analogies found in the literature, and clarify the connection between them.
Special emphasis is placed in two exact physical analogies: the analogy based
on inertial fields from the so-called "1+3 formalism", and the analogy based on
tidal tensors. Both are reformulated, extended and generalized. We write in
both formalisms the Maxwell and the full exact Einstein field equations with
sources, plus the algebraic Bianchi identities, which are cast as the
source-free equations for the gravitational field. New results within each
approach are unveiled. The well known analogy between linearized gravity and
electromagnetism in Lorentz frames is obtained as a limiting case of the exact
ones. The formal analogies between the Maxwell and Weyl tensors are also
discussed, and, together with insight from the other approaches, used to
physically interpret gravitational radiation. The precise conditions under
which a similarity between gravity and electromagnetism occurs are discussed,
and we conclude by summarizing the main outcome of each approach.Comment: 60 pages, 2 figures. Improved version (compared to v2) with some
re-write, notation improvements and a new figure that match the published
version; expanded compared to the published version to include Secs. 2.3 and
Searches for Gravitational Waves from Binary Neutron Stars: A Review
A new generation of observatories is looking for gravitational waves. These
waves, emitted by highly relativistic systems, will open a new window for ob-
servation of the cosmos when they are detected. Among the most promising
sources of gravitational waves for these observatories are compact binaries in
the final min- utes before coalescence. In this article, we review in brief
interferometric searches for gravitational waves emitted by neutron star
binaries, including the theory, instru- mentation and methods. No detections
have been made to date. However, the best direct observational limits on
coalescence rates have been set, and instrumentation and analysis methods
continue to be refined toward the ultimate goal of defining the new field of
gravitational wave astronomy.Comment: 30 pages, 5 Figures, to appear in "Short-Period Binary Stars:
Observations, Analyses, and Results", Ed.s Eugene F. Milone, Denis A. Leahy,
David W. Hobil
Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
The article reviews the current status of a theoretical approach to the
problem of the emission of gravitational waves by isolated systems in the
context of general relativity. Part A of the article deals with general
post-Newtonian sources. The exterior field of the source is investigated by
means of a combination of analytic post-Minkowskian and multipolar
approximations. The physical observables in the far-zone of the source are
described by a specific set of radiative multipole moments. By matching the
exterior solution to the metric of the post-Newtonian source in the near-zone
we obtain the explicit expressions of the source multipole moments. The
relationships between the radiative and source moments involve many non-linear
multipole interactions, among them those associated with the tails (and
tails-of-tails) of gravitational waves. Part B of the article is devoted to the
application to compact binary systems. We present the equations of binary
motion, and the associated Lagrangian and Hamiltonian, at the third
post-Newtonian (3PN) order beyond the Newtonian acceleration. The
gravitational-wave energy flux, taking consistently into account the
relativistic corrections in the binary moments as well as the various tail
effects, is derived through 3.5PN order with respect to the quadrupole
formalism. The binary's orbital phase, whose prior knowledge is crucial for
searching and analyzing the signals from inspiralling compact binaries, is
deduced from an energy balance argument.Comment: 109 pages, 1 figure; this version is an update of the Living Review
article originally published in 2002; available on-line at
http://www.livingreviews.org
General Relativistic Gravity Gradiometry
Gravity gradiometry within the framework of the general theory of relativity
involves the measurement of the elements of the relativistic tidal matrix,
which is theoretically obtained via the projection of the spacetime curvature
tensor upon the nonrotating orthonormal tetrad frame of a geodesic observer.
The behavior of the measured components of the curvature tensor under Lorentz
boosts is briefly described in connection with the existence of certain special
tidal directions. Relativistic gravity gradiometry in the exterior
gravitational field of a rotating mass is discussed and a gravitomagnetic beat
effect along an inclined spherical geodesic orbit is elucidated.Comment: 18 pages, invited contribution to appear in "Relativistic Geodesy:
Foundations and Applications", D. Puetzfeld et al. (eds.), 2018; v2: matches
version published in: D. Puetzfeld and C. L\"ammerzahl (eds.) "Relativistic
Geodesy" (Springer, Cham, 2019), pp. 143-15
Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
Shear-free or asymptotically shear-free null geodesic congruences possess a
large number of fascinating geometric properties and to be closely related, in
the context of general relativity, to a variety of physically significant
affects. It is the purpose of this paper to develop these issues and find
applications in GR. The applications center around the problem of extracting
interior physical properties of an asymptotically flat space-time directly from
the asymptotic gravitational (and Maxwell) field itself in analogy with the
determination of total charge by an integral over the Maxwell field at infinity
or the identification of the interior mass (and its loss) by (Bondi's)
integrals of the Weyl tensor, also at infinity. More specifically we will see
that the asymptotically shear-free congruences lead us to an asymptotic
definition of the center-of-mass and its equations of motion. This includes a
kinematic meaning, in terms of the center of mass motion, for the Bondi
three-momentum. In addition, we obtain insights into intrinsic spin and, in
general, angular momentum, including an angular momentum conservation law with
well-defined flux terms. When a Maxwell field is present the asymptotically
shear-free congruences allow us to determine/define at infinity a
center-of-charge world-line and intrinsic magnetic dipole moment.Comment: 98 pages, 6 appendices. v2: typos corrected; v3: significant changes
made to results section using simpler arguments, added discussion of real
structures, additional references, 2 new appendice
The EROS2 search for microlensing events towards the spiral arms: the complete seven season results
The EROS-2 project has been designed to search for microlensing events
towards any dense stellar field. The densest parts of the Galactic spiral arms
have been monitored to maximize the microlensing signal expected from the stars
of the Galactic disk and bulge. 12.9 million stars have been monitored during 7
seasons towards 4 directions in the Galactic plane, away from the Galactic
center. A total of 27 microlensing event candidates have been found. Estimates
of the optical depths from the 22 best events are provided. A first order
interpretation shows that simple Galactic models with a standard disk and an
elongated bulge are in agreement with our observations. We find that the
average microlensing optical depth towards the complete EROS-cataloged stars of
the spiral arms is , a number that is
stable when the selection criteria are moderately varied. As the EROS catalog
is almost complete up to , the optical depth estimated for the
sub-sample of bright target stars with () is easier to interpret. The set of microlensing events
that we have observed is consistent with a simple Galactic model. A more
precise interpretation would require either a better knowledge of the distance
distribution of the target stars, or a simulation based on a Galactic model.
For this purpose, we define and discuss the concept of optical depth for a
given catalog or for a limiting magnitude.Comment: 22 pages submitted to Astronomy & Astrophysic
Measuring the gravitational field in General Relativity: From deviation equations and the gravitational compass to relativistic clock gradiometry
How does one measure the gravitational field? We give explicit answers to
this fundamental question and show how all components of the curvature tensor,
which represents the gravitational field in Einstein's theory of General
Relativity, can be obtained by means of two different methods. The first method
relies on the measuring the accelerations of a suitably prepared set of test
bodies relative to the observer. The second methods utilizes a set of suitably
prepared clocks. The methods discussed here form the basis of relativistic
(clock) gradiometry and are of direct operational relevance for applications in
geodesy.Comment: To appear in "Relativistic Geodesy: Foundations and Application", D.
Puetzfeld et. al. (eds.), Fundamental Theories of Physics, Springer 2018, 52
pages, in print. arXiv admin note: text overlap with arXiv:1804.11106,
arXiv:1511.08465, arXiv:1805.1067