Time delay in the quadrupole field of a body at rest in the 2PN approximation

Zschocke, Sven

doi:10.1103/physrevd.106.104052

Cited by 2 publications

(12 citation statements)

References 87 publications

(367 reference statements)

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“…Then, using the basic integral (25) in [16], one finds for the second integration the formula given by Eq. ( 27) in [16], which leads to the solution for the second integration of geodesic equation (36).…”

Section: Time Delay In Field Of An Arbitrary Bodymentioning

confidence: 99%

“…Note, that in stationary case the geodesic equation in 1.5PN approximation of the post-Newtonian (PN) scheme and the geodesic equation in 1PM approximation of the post-Minkowskian (PM) scheme agree with each other [30]. By inserting the metric perturbation (15) into the geodesic equation (36), one may separate the geodesic equation into a canonical term, ẍcan , plus a gauge term, ẍgauge , as follows:…”

Section: B Geodesic Equationmentioning

confidence: 99%

“…(40) In particular, one has to insert the multipole decomposition of the metric perturbations (15) into the geodesic equation (36) and then one has to apply advanced integration methods developed in [16], which yields…”

Section: B Geodesic Equationmentioning

confidence: 99%

“…In [16] advanced integration methods have been introduced that one allow to integrate (36) exactly. The basic ideas of the conception has originally been introduced in [16] for bodies with time-independent multipoles and where the center of mass of the body is assumed to be at rest with respect to the harmonic coordinate system.…”

Section: Time Delay In Field Of An Arbitrary Bodymentioning

confidence: 99%

“…and P ij ξ j by the spatial components of the impact vector d i σ . Further details about this approach can be found in [16,32,36].…”

Section: Time Delay In Field Of An Arbitrary Bodymentioning

confidence: 99%

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Total light deflection in the gravitational field of an axisymmetric body at rest with full mass and spin multipole structure

Zschocke

2023

Phys. Rev. D

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The time delay of a light signal which propagates in the gravitational field of an isolated body is considered. The body can be of arbitrary but time-independent shape and inner structure and can be in uniform rotational motion, while the center of mass of the body is assumed to be at rest. The gravitational field is given in the post-Newtonian scheme and in terms of the full set of mass-multipoles and spin-multipoles of the body. The asymptotic configuration is considered, where source and observer are located at spatial infinity from the massive body. It is found that in this asymptotic limit the higher multipole terms of time delay are related to the higher multipole terms of total light deflection. Furthermore, it is shown that the gauge terms vanish in this asymptotic configuration. In case of an axisymmetric body in uniform rotational motion, the higher multipole terms of time delay can be expressed in terms of Chebyshev polynomials. This fact allows one to determine the upper limits of the time delay for higher multipoles. These upper limits represent a criterion to identify those multipoles which contribute significantly to the time delay for a given accuracy of time measurements. It is found that the first mass-multipoles with l ≤ 8 and the first spin-multipoles with l ≤ 3 are sufficient for an accuracy on the femto-second scale of accuracy in time measurements.

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