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

Abstract

In this investigation the boundary value problem of light propagation in the gravitational field of one arbitrarily moving body with monopole structure is considered in the second post-Newtonian approximation. The solution of the boundary value problem comprises a set of altogether three transformations: k -> sigma and sigma -> n and k -> n. Analytical solutions of these transformations are given and the upper limit of each individual term is determined. Based on these results, simplified transformations are obtained by keeping only those terms relevant for the given goal accuracy of 1 nano-arcsecond in light deflection. Like in case of light propagation in the gravitational field of one body at rest, there are so-called enhanced terms which are of second post-Newtonian order but contain one and the same typical large numerical factor. Finally, the impact of enhanced terms beyond 2PN approximation is considered. It is found that enhanced 3PN terms are relevant for astrometry on the level of 1 nano-arcsecond in light deflection, while enhanced 4PN terms are negligible, except for grazing rays at the Sun.

68 pages, 4 figures

References in corpus (33)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Gaia Data Release 2. Summary of the contents and survey properties
• The Gaia mission
• The Confrontation between General Relativity and Experiment
• Multi-messenger Observations of a Binary Neutron Star Merger
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Gaia Data Release 1. Summary of the astrometric, photometric, and survey properties
• Gaia Data Release 2: using Gaia parallaxes
• Gaia Data Release 1: Astrometry - one billion positions, two million proper motions and parallaxes
• Gaia Data Release 2: The Celestial reference frame (Gaia-CRF2)
• General post-Minkowskian expansion of time transfer functions
• Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers
• The Speed of Gravity in General Relativity and Theoretical Interpretation of the Jovian Deflection Experiment
• High precision astrometry with a diffractive pupil telescope
• Aberration and the Fundamental Speed of Gravity in the Jovian Deflection Experiment
• The Second Post-Newtonian Light Propagation and Its Astrometric Measurement in the Solar System
• GaiaNIR: Combining optical and Near-Infra-Red (NIR) capabilities with Time-Delay-Integration (TDI) sensors for a future Gaia-like mission
• Light propagation in the field of a moving axisymmetric body: theory and application to JUNO
• Second-order time delay by a radially moving Kerr-Newman black hole
• Scalar-tensor propagation of light in the inner solar system at the millimetric level
• The Post-Newtonian Treatment of the VLBI Experiment on September 8, 2002
• Second post-Newtonian approximation of Einstein-aether theory
• The gravitational time delay in the field of a slowly moving body with arbitrary multipoles
• Light propagation in the gravitational field of N arbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry
• Second Order Kerr-Newman Time Delay
• Light propagation in the gravitational field of one arbitrarily moving pointlike body in the 2PN approximation
• Gravitational field of one uniformly moving extended body and N arbitrarily moving pointlike bodies in post-Minkowskian approximation
• Light propagation in 2PN approximation in the field of one moving monopole: I. Initial value problem
• The speed of gravity has not been measured from time delays
• On the Speed of Gravity and Relativistic v/c Corrections to the Shapiro Time Delay
• Comments on the paper by S. Samuel "On the speed of gravity and the Jupiter/Quasar measurement"
• Forthcoming Close Angular Approaches of Planets to Radio Sources and Possibilities to Use Them as GR Tests
• Comments on "Measuring the Gravity Speed by VLBI"

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