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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a complete analysis of the light rays within the linearized,weak-field approximation of a Schwarzschild-like metric describing thegravitational field of an isolated, spherically symmetric body. We prove inthis context the existence of two time transfer functions and we obtain thesefunctions in an exact closed-form. We are led to distinguish two regimes. Inthe first regime, the two time transfer functions correspond to rays which areconfined in regions of spacetime where the weak-field approximation is valid.Such a regime occurs in gravitational lensing configurations with double imagesof a given source. We find the general expressions of the angular separationand the difference in light travel time between the two images. In the secondregime, there exists only one time transfer function corresponding to a lightray remaining in a region of weak field. Performing a Taylor expansion of thisfunction with respect to the gravitational constant, we obtain the Shapiro timedelay completed by a series of so-called "enhanced terms". The enhanced termsbeyond the third order are new.

Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects