English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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

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