Post-Newtonian limitations on measurement of the PPN parameters caused by motion of gravitating bodies

Kopeikin, Sergei M.

doi:10.1111/j.1365-2966.2009.15387.x

Cited by 25 publications

(31 citation statements)

References 42 publications

(114 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We must now determine these constants in such a way as to satisfy the boundary conditions. For this to be possible, one must be able to express the potentials e Π (i) and m Π (i) of the incident wave in a series of the from (70). To proceed with the solution of the scattering problem, we consider the incident wave given by (40)- (41).…”

Section: A Representing the Field In Terms Of Debye Potentialsmentioning

confidence: 99%

See 1 more Smart Citation

Diffraction of electromagnetic waves in the gravitational field of the Sun

2017

View full text Add to dashboard Cite

We consider the propagation of electromagnetic (EM) waves in the gravitational field of the Sun within the first post-Newtonian approximation of the general theory of relativity. We solve Maxwell's equations for the EM field propagating on the background of a static mass monopole and find an exact closed form solution for the Debye potentials, which, in turn, yield a solution to the problem of diffraction of EM waves in the gravitational field of the Sun. The solution is given in terms of the confluent hypergeometric function and, as such, it is valid for all distances and angles. Using this solution, we develop a wave-theoretical description of the solar gravitational lens (SGL) and derive expressions for the EM field and energy flux in the immediate vicinity of the focal line of the SGL. Aiming at the potential practical applications of the SGL, we study its optical properties and discuss its suitability for direct high-resolution imaging of a distant exoplanet.PACS numbers: 03.30.+p, 04.25.Nx, 06.30.Gv, 95.10.Eg, 95.10.Jk, 95.55.Pe

show abstract

Section: A Representing the Field In Terms Of Debye Potentialsmentioning

confidence: 99%

“…In geometric optics, the phase ϕ is a scalar function, a solution to the eikonal equation [3,31,42,70]:…”

Section: Geometric Optics Approximation For the Wave Propagation In Tmentioning

confidence: 99%

Diffraction of electromagnetic waves in the gravitational field of the Sun

2017

View full text Add to dashboard Cite

show abstract

“…Velocity effects on the second-order gravitational delay may influence on the high-precision measurements of some crucial parameters, such as the post-Newtonian parameters [7][8][9], and Hubble's constant when measured via the time delay between two lensed images [35][36][37][38]. For example, the relation between the time delay and the post-Newtonian parameters in the timedependent gravitational field has been given in Ref.…”

Section: Possible Applications and Detection Of The Velocity Effementioning

confidence: 99%

“…The time dependence of a background field caused by the translational motion of a gravitational source usually exerts an influence on the propagation of electromagnetic waves. This kind of kinematical effect (also called the velocity effect [1]) on the gravitational time delay of light has been investigated in detail in the last two decades [2][3][4][5][6][7][8][9][10][11]. In particular, Kopeikin and Schäfer [2] pioneered the Lorentz-covariant theory for light propagating in the gravitational field of an ensemble of arbitrarily moving bodies, in which the generalized form of the Shapiro time delay [12,13] was obtained in the first post-Minkowskian (1PM) approximation.…”

Section: Introductionmentioning

confidence: 99%

Second-order time delay by a radially moving Kerr-Newman black hole

Lin

2016

Phys. Rev. D

View full text Add to dashboard Cite

We derive the analytical time delay of light propagating in the equatorial plane and parallel to the velocity of a moving Kerr-Newman black hole up to the second post-Minkowskian order via integrating the null geodesic equations. The velocity effects are expressed by a very compact form. We then concentrate on analyzing the magnitudes of the correctional effects on the second-order contributions to the delay and discuss their possible detection. Our result in the first post-Minkowskian approximation is in agreement with Kopeikin and Schäfer's formulation which is based on the retarded Liénard-Wiechert potential.

show abstract

“…In the geometric optics approximation, the phase ϕ is found as a solution to the eikonal equation [5,[8][9][10][11]:…”

Section: B Geometric Optics Approximation For the Wave Propagation Imentioning

confidence: 99%

General relativistic laser interferometric observables of the GRACE-Follow-On mission

2014

View full text Add to dashboard Cite

We develop a high-precision model for laser ranging interferometric (LRI) observables of the GRACE Follow-On (GRACE-FO) mission. For this, we study the propagation of an electromagnetic wave in the gravitational field in the vicinity of an extended body, in the post-Newtonian approximation of the general theory of relativity. We present a general relativistic model for the phase of a plane wave that accounts for contributions of all the multipoles of the gravitating body, its angular momentum, as well as the contribution of tidal fields produced by external sources. We develop a new approach to model a coherent signal transmission in the gravitational field of the solar system that relies on a relativistic treatment of the phase. We use this approach to describe high-precision interferometric measurements on GRACE-FO and formulate the key LRI observables, namely the phase and phase rate of a coherent laser link between the two spacecraft. We develop a relativistic model for the LRI-enabled range between the two GRACE-FO spacecraft, accurate to less than 1 nm, and a high-precision model for the corresponding range rate, accurate to better than 0.1 nm/s. We also formulate high-precision relativistic models for the double one-way range (DOWR) and DOWR-enabled range rate observables originally used on GRACE and now studied for interferometric measurements on GRACE-FO. Our formulation justifies the basic assumptions behind the design of the GRACE-FO mission and highlights the importance of achieving nearly circular and nearly identical orbits for the GRACE-FO spacecraft.

show abstract

Post-Newtonian limitations on measurement of the PPN parameters caused by motion of gravitating bodies

Cited by 25 publications

References 42 publications

Diffraction of electromagnetic waves in the gravitational field of the Sun

Diffraction of electromagnetic waves in the gravitational field of the Sun

Second-order time delay by a radially moving Kerr-Newman black hole

General relativistic laser interferometric observables of the GRACE-Follow-On mission

Contact Info

Product

Resources

About