Light propagation in 2PN approximation in the field of one moving monopole II. Boundary value problem

Zschocke, Sven

doi:10.1088/1361-6382/aaeb4c

Cited by 7 publications

(9 citation statements)

References 121 publications

(631 reference statements)

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“…(29) and using Eqs. (34) and (35). Here it is sufficient to consider only the first two orders, given by [82] (to verify that agreement one has to adopt a flat background metric in [82]).…”

Section: A the Post-minkowskian Expansion Of The Metric Tensormentioning

confidence: 96%

Post-linear metric of a compact source of matter

Zschocke

2019

Phys. Rev. D

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The Multipolar Post-Minkowskian (MPM) formalism represents an approach for determining the metric density in the exterior of a compact source of matter. In the MPM formalism the metric density is given in harmonic coordinates and in terms of symmetric tracefree (STF) multipoles. In this investigation, the post-linear metric density of this formalism is used in order to determine the post-linear metric tensor in the exterior of a compact source of matter. The metric tensor is given in harmonic coordinates and in terms of STF multipoles. The post-linear metric coefficients are associated with an integration procedure. The integration of these post-linear metric coefficients is performed explicitly for the case of a stationary source, where the first multipoles (monopole and quadrupole) of the source are taken into account. These studies are a requirement for further investigations in the theory of light propagation aiming at highly precise astrometric measurements in the solar system, where the post-linear coefficients of the metric tensor of solar system bodies become relevant.

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“…(29) and using Eqs. (34) and (35). Here it is sufficient to consider only the first two orders, given by [82] (to verify that agreement one has to adopt a flat background metric in [82]).…”

Section: A the Post-minkowskian Expansion Of The Metric Tensormentioning

confidence: 96%

Post-linear metric of a compact source of matter

Zschocke

2019

Phys. Rev. D

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“…These individual terms are given by Eqs. (E16), (E18), (E19), (E20), (E21), (E22), (E23), (E24), (E25), (E26) in Appendix E. Similar to (47), the sum of these terms in (73) can be separated into monopole and quadrupole and mixed monopole-quadrupole terms,…”

Section: B the Geodesic Equation In 2pn Approximationmentioning

confidence: 99%

Light propagation in 2PN approximation in the monopole and quadrupole field of a body at rest: Initial value problem

Zschocke

2022

Preprint

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The light trajectory in the gravitational field of one body at rest with monopole and quadrupole structure is determined in the second post-Newtonian (2PN) approximation. The terms in the geodesic equation for light rays are separated into time-independent tensorial coefficients and four kind of time-dependent scalar functions. Accordingly, the first and second integration of geodesic equation can be reduced in each case to only four kind of scalar master integrals. These integrals can be solved in closed form by recurrence relations. The 2PN terms of monopole and quadrupole contribute less than 1 nano-arcsecond to the total light deflection. There are, however, enhanced terms in the 2PN light deflection, both in case of monopole and quadrupole. These enhanced 2PN terms are caused by the use of an impact vector which is indispensable for modeling of real astrometric measurements. In case of grazing light rays at Jupiter and Saturn, the enhanced 2PN terms, caused by the quadrupole structure of the body, amount up to 0.95 micro-arcseconds and 0.29 micro-arcseconds, respectively. Thus, the 2PN quadrupole terms are relevant for high-precision astrometry on the sub-micro-arcsecond scale of accuracy.

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“…The light propagation in the gravitational filed can be studied by null geodesic Eqs. [72,73,74,75] or time transfer functions [76,77,78,79]. Some solutions have been proposed in the post-Minkowskian and post-Newtonian approximations in the Solar System.…”

Section: Appendix a Time Transfer Functionmentioning

confidence: 99%

Relativistic tidal effects on clock-comparison experiments

Qin

Tan

Shao

2019

Class. Quantum Grav.

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We consider the relativistic tidal effects on frequency shift of clockcomparison experiments. The relativistic formulation for frequency shift and time transfer is derived in the gravitational field of a tidal, axisymmetric, and rotating Earth. With the help of Love numbers describing the tidal response of solid Earth, we formulize the mathematical connection between tidal effects from the ground-based clock-comparison experiments and the local gravity tides from the gravimeters, which in turn provides us an approach to eliminate tidal influences on clock comparison with the local gravity tides data. Moreover, we develop a method of the perturbed Kepler orbit to determine relativistic effects of clock comparison for space missions, which allows more precise calculations comparing to the conventional method of unperturbed Kepler orbit. With this perturbed method, it can give the perturbation of relativistic effects due to the orbital changes under the influences of tidal forces, Earth's oblateness etc. In addition, as the applications of our results, we simulate tidal effects in frequency shift for the clock comparison on the ground and also give some estimates for TianQin mission and GPS.

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Light propagation in 2PN approximation in the field of one moving monopole II. Boundary value problem

Cited by 7 publications

References 121 publications

Post-linear metric of a compact source of matter

Post-linear metric of a compact source of matter

Light propagation in 2PN approximation in the monopole and quadrupole field of a body at rest: Initial value problem

Relativistic tidal effects on clock-comparison experiments

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