Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation

Abstract

A procedure avoiding any integration of the null geodesic equations is used to derive the direction of light propagation in a three-parameter family of static, spherically symmetric spacetimes within the post-post-Minkowskian approximation. Quasi-Cartesian isotropic coordinates adapted to the symmetries of spacetime are systematically used. It is found that the expression of the angle formed by two light rays as measured by a static observer staying at a given point is remarkably simple in these coordinates. The attention is mainly focused on the null geodesic paths that we call the "quasi-Minkowskian light rays". The vector-like functions characterizing the direction of propagation of such light rays at their points of emission and reception are firstly obtained in the generic case where these points are both located at a finite distance from the centre of symmetry. The direction of propagation of the quasi-Minkowskian light rays emitted at infinity is then straightforwardly deduced. An intrinsic definition of the gravitational deflection angle relative to a static observer located at a finite distance is proposed for these rays. The expression inferred from this definition extends the formula currently used in VLBI astrometry up to the second order in the gravitational constant G.

19 pages; revised introduction; added references for introduction; corrected typos; published in Class. Quantum Grav

References in corpus (3)

• General post-Minkowskian expansion of time transfer functions
• A general relativistic model for the light propagation in the gravitational field of the Solar System: the dynamical case
• Scalar-tensor propagation of light in the inner solar system at the millimetric level

Cited by in corpus (19)

• Relativistic formulation of coordinate light time, Doppler and astrometric observables up to the second post-Minkowskian order
• 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
• Time Transfer functions as a way to validate light propagation solutions for space astrometry
• New method for determining the light travel time in static, spherically symmetric spacetimes. Calculation of the terms of order $G^3$
• Light propagation in the gravitational field of N arbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry
• Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects
• Relativistic tidal effects on clock-comparison experiments
• Light propagation in the gravitational field of one arbitrarily moving pointlike body in the 2PN approximation
• Light propagation in 2PN approximation in the field of one moving monopole: I. Initial value problem
• Light propagation in 2PN approximation in the field of one moving monopole II. Boundary value problem
• General expansion of time transfer functions in optical spacetime
• The Science of Fundamental Catalogs
• Relativistic modeling of atmospheric occultations with time transfer functions
• Light propagation in 2PN approximation in the monopole and quadrupole field of a body at rest: Initial value problem
• Post-linear metric of a compact source of matter
• Bilocal geodesic operators in static spherically-symmetric spacetimes
• Total light deflection in the gravitational field of an axisymmetric body at rest with full mass and spin multipole structure
• Post-Minkowskian solution for the small-deflection motion of test particles in Kerr-Newman spacetime