World function and time transfer: general post-Minkowskian expansions

Poncin-Lafitte, Christophe Le; Linet, B.; Teyssandier, P.

doi:10.1088/0264-9381/21/18/012

Cited by 72 publications

(172 citation statements)

References 31 publications

Supporting

Mentioning

167

Contrasting

Order By: Relevance

“…We recover a result previously derived by different approaches [10,14] (see also Refs. [11] and [12] in the case where β = γ = δ = 1).…”

supporting

confidence: 89%

“…The derivation of the time transfer function performed here for a static, spherically symmetric space-time is significantly more simple than the calculation carried out in Ref. [14]. As a final remark, it may be noted that since the time transfer functions are sufficient to determine the deflection and the frequency shift of a light signal, the systematic method developed here will be very convenient to tackle the relativistic problems raised by highly accurate astrometry and time/frequency metrology.…”

Section: Discussionmentioning

confidence: 89%

“…[14] and [15]. § Equations (4) and (5) can also be derived from the general-relativistic version of Fermat's principle established in Ref.…”

Section: Time Transfer Functionsmentioning

confidence: 99%

See 2 more Smart Citations

General post-Minkowskian expansion of time transfer functions

Teyssandier¹,

Poncin-Lafitte²

2008

Class. Quantum Grav.

Self Cite

100

175

View full text Add to dashboard Cite

Abstract. Modeling most of the tests of general relativity requires to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant G (general post-Minkowskian expansion). Our method is self-sufficient, in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function are necessary. To illustrate the method, the time transfer function of a threeparameter family of static, spherically symmetric metrics is derived within the post-linear approximation.

show abstract

“…We recover a result previously derived by different approaches [10,14] (see also Refs. [11] and [12] in the case where β = γ = δ = 1).…”

supporting

confidence: 89%

Section: Discussionmentioning

confidence: 89%

See 1 more Smart Citation

General post-Minkowskian expansion of time transfer functions

Teyssandier¹,

Poncin-Lafitte²

2008

Class. Quantum Grav.

Self Cite

100

175

View full text Add to dashboard Cite

show abstract

“…In Ref. [6], Le Poncin-Lafitte et al have recently developed an alternative approach to the problem of light deflection and time/frequency transfer in post-Minkowskian gravitational fields based on an expansion of the Synge world function for null geodesics. In that paper the world function and time transfer function were computed for a static spherically symmetric body to the second post-Minkowskian approximation.…”

Section: Introductionmentioning

confidence: 99%

Light deflection in the postlinear gravitational field of bounded pointlike masses

Brügmann

2005

Phys. Rev. D

View full text Add to dashboard Cite

Light deflection in the post-linear gravitational field of two bounded point-like masses is treated. Both the light source and the observer are assumed to be located at infinity in an asymptotically flat space. The equations of light propagation are explicitly integrated to the second order in G/c 2 . Some of the integrals are evaluated by making use of an expansion in powers of the ratio of the relative separation distance to the impact parameter (r12/ξ). A discussion of which orders must be retained to be consistent with the expansion in terms of G/c 2 is given. It is shown that the expression obtained in this paper for the angle of light deflection is fully equivalent to the expression obtained by Kopeikin and Schäfer up to the order given there. The deflection angle takes a particularly simple form for a light ray originally propagating orthogonal to the orbital plane of a binary with equal masses. Application of the formulae for the deflection angle to the double pulsar PSR J0737-3039 for an impact parameter five times greater than the relative separation distance of the binary's components shows that the corrections to the Epstein-Shapiro light deflection angle of about 10 −6 arcsec lie between 10 −7 and 10 −8 arcsec.PACS numbers: 04.20.Cv, 04.25.-g, 04.25.Nx I. INTRODUCTIONLight deflection by a gravitational field [1] is one of the observational cornerstones of general relativity. The observational confirmation of Einstein's prediction that light would be deflected by the gravitational field of the Sun [2] brought general relativity to the attention of the general public in the 1920's. Today, technology has reached a level at which the extremely high precision of current ground-based radio interferometric astronomical observations approaches 1 µarcsec and within the next decade the accuracy of space-based astrometric positional observations is also expected to reach this accuracy. At this level of accuracy we can no longer treat the gravitational field of a system of moving bodies as static and spherically symmetric. This fact is one of the principal reasons for the necessity of a more accurate solution to the problem of the propagation of electromagnetic waves in non-stationary gravitational fields of celestial bodies. To reach the accuracy of 1 µarcsec, many subtle relativistic effects must be taken into account in the treatment of light propagation in non-stationary gravitational fields of moving bodies. One of the most intricate problems is the computation of the effects of translational motion of the gravitating bodies on light propagation.This question was treated for the first time by Hellings in 1986 [3]. In 1989 Klioner [4] solved the problem completely to the first post-Newtonian (1PN) order (i.e. to the order 1/c2 ) for the case of bodies moving with constant velocity. The complete solution of the problem for arbitrarily moving bodies in the first post-Minkowskian approximation (linear in the gravitational constant G) was found by Kopeikin and Schäfer in 1999 [5]. They succeeded in integrating...

show abstract

“…Some of the concepts that are being reviewed carefully are those involving light signal propagation (Klioner 2003;Le Poncin-Lafitte et al 2004) and the description of the astronomical sources and observers (Klioner 2004) in the context of the IAU resolutions (Soffel et al 2003) that aim to define a consistent framework to model astronomical observations. This effort involves many groups and individuals around the world and one relevant aspect is the appropriate description of stellar motion.…”

Section: Introduction and Notationmentioning

confidence: 99%

Astrometric light-travel time signature of sources in nonlinear motion

Anglada-Escudé¹,

Torra²

2006

A&A

View full text Add to dashboard Cite

Context. Very precise planned space astrometric missions and recent improvements in imaging capabilities require a detailed review of the assumptions of classical astrometric modeling. Aims. We show that Light-Travel Time must be taken into account in modeling the kinematics of astronomical objects in nonlinear motion, even at stellar distances. Methods. A closed expression to include Light-Travel Time in the current astrometric models with nonlinear motion is provided. Using a perturbative approach the expression of the Light-Travel Time signature is derived. We propose a practical form of the astrometric modelling to be applied in astrometric data reduction of sources at stellar distances(d > 1 pc). Results. We show that the Light-Travel Time signature is relevant at µas accuracy (or even at mas) depending on the time span of the astrometric measurements. We explain how information on the radial motion of a source can be obtained. Some estimates are provided for known nearby binary systems Conclusions. Given the obtained results, it is clear that this effect must be taken into account in interpreting precise astrometric measurements. The effect is particularly relevant in measurements performed by the planned astrometric space missions (GAIA, SIM, JASMINE, TPF/DARWIN). An objective criterion is provided to quickly evaluate whether the Light-Travel Time modeling is required for a given source or system.

show abstract

World function and time transfer: general post-Minkowskian expansions

Cited by 72 publications

References 31 publications

General post-Minkowskian expansion of time transfer functions

General post-Minkowskian expansion of time transfer functions

Light deflection in the postlinear gravitational field of bounded pointlike masses

Astrometric light-travel time signature of sources in nonlinear motion

Contact Info

Product

Resources

About