19 research outputs found
The gravitational time delay in the field of a slowly moving body with arbitrary multipoles
We calculate the time delay of light in the gravitational field of a slowly
moving body with arbitrary multipoles (mass and spin multipole moments) by the
Time-Transfer-Function (TTF) formalism. The parameters we use, first introduced
by Kopeikin for a gravitational source at rest, make the integration of the TTF
very elegant and simple. Results completely coincide with expressions from the
literature. The results for a moving body (with constant velocity) with
complete multipole-structure are new, according to our knowledge.Comment: 9 pages, no figure
Relativistic theory of elastic deformable astronomical bodies: perturbation equations in rotating spherical coordinates and junction conditions
In this paper, the dynamical equations and junction conditions at the
interface between adjacent layers of different elastic properties for an
elastic deformable astronomical body in the first post-Newtonian approximation
of Einstein theory of gravity are discussed in both rotating Cartesian
coordinates and rotating spherical coordinates. The unperturbed rotating body
(the ground state) is described as uniformly rotating, stationary and
axisymmetric configuration in an asymptotically flat space-time manifold.
Deviations from the equilibrium configuration are described by means of a
displacement field. In terms of the formalism of relativistic celestial
mechanics developed by Damour, Soffel and Xu, and the framework established by
Carter and Quintana the post Newtonian equations of the displacement field and
the symmetric trace-free shear tensor are obtained. Corresponding
post-Newtonian junction conditions at interfaces also the outer surface
boundary conditions are presented. The PN junction condition is an extension of
Wahr's one which is a Newtonian junction conditions without rotating.Comment: Revtex4, 14 page
Relativistic Celestial Mechanics with PPN Parameters
Starting from the global parametrized post-Newtonian (PPN) reference system
with two PPN parameters and we consider a space-bounded
subsystem of matter and construct a local reference system for that subsystem
in which the influence of external masses reduces to tidal effects. Both the
metric tensor of the local PPN reference system in the first post-Newtonian
approximation as well as the coordinate transformations between the global PPN
reference system and the local one are constructed in explicit form. The terms
proportional to reflecting a violation of the
equivalence principle are discussed in detail. We suggest an empirical
definition of multipole moments which are intended to play the same role in PPN
celestial mechanics as the Blanchet-Damour moments in General Relativity.
Starting with the metric tensor in the local PPN reference system we derive
translational equations of motion of a test particle in that system. The
translational and rotational equations of motion for center of mass and spin of
each of extended massive bodies possessing arbitrary multipole structure
are derived. As an application of the general equations of motion a
monopole-spin dipole model is considered and the known PPN equations of motion
of mass monopoles with spins are rederived.Comment: 71 page
Age of the Universe: Influence of the Inhomogeneities on the global Expansion-Factor
For the first time we calculate quantitatively the influence of
inhomogeneities on the global expansion factor by averaging the Friedmann
equation. In the framework of the relativistic second-order
Zel'dovich-approximation scheme for irrotational dust we use observational
results in form of the normalisation constant fixed by the COBE results and we
check different power spectra, namely for adiabatic CDM, isocurvature CDM, HDM,
WDM, Strings and Textures. We find that the influence of the inhomogeneities on
the global expansion factor is very small. So the error in determining the age
of the universe using the Hubble constant in the usual way is negligible. This
does not imply that the effect is negligible for local astronomical
measurements of the Hubble constant. Locally the determination of the
redshift-distance relation can be strongly influenced by the peculiar velocity
fields due to inhomogeneities. Our calculation does not consider such effects,
but is contrained to comparing globally homogeneous and averaged inhomogeneous
matter distributions. In addition we relate our work to previous treatments.Comment: 10 pages, version accepted by Phys. Rev.
Applied general relativity: theory and applications in astronomy, celestial mechanics and metrology
In the late 20th and beginning 21st century high-precision astronomy, positioning and metrology strongly rely on general relativity. Supported by exercises and solutions this book offers graduate students and researchers entering those fields a self-contained and exhaustive but accessible treatment of applied general relativity. The book is written in a homogenous (graduate level textbook) style allowing the reader to understand the arguments step by step. It first introduces the mathematical and theoretical foundations of gravity theory and then concentrates on its general relativistic applications: clock rates, clock sychronization, establishment of time scales, astronomical references frames, relativistic astrometry, celestial mechanics and metrology. The authors present up-to-date relativistic models for applied techniques such as Satellite LASER Ranging (SLR), Lunar LASER Ranging (LLR), Globale Navigation Satellite Systems (GNSS), Very Large Baseline Interferometry (VLBI), radar measurements, gyroscopes and pulsar timing. A list of acronyms helps the reader keep an overview and a mathematical appendix provides required functions and terms