7 research outputs found
A universal tool for determining the time delay and the frequency shift of light: Synge's world function
In almost all of the studies devoted to the time delay and the frequency
shift of light, the calculations are based on the integration of the null
geodesic equations. However, the above-mentioned effects can be calculated
without integrating the geodesic equations if one is able to determine the
bifunction giving half the squared geodesic distance between
two points and (this bifunction may be called Synge's world
function). In this lecture, is determined up to the order
within the framework of the PPN formalism. The case of a stationary
gravitational field generated by an isolated, slowly rotating axisymmetric body
is studied in detail. The calculation of the time delay and the frequency shift
is carried out up to the order . Explicit formulae are obtained for the
contributions of the mass, of the quadrupole moment and of the internal angular
momentum when the only post-Newtonian parameters different from zero are
and . It is shown that the frequency shift induced by the mass
quadrupole moment of the Earth at the order will amount to
in spatial experiments like the ESA's Atomic Clock Ensemble in Space mission.
Other contributions are briefly discussed.Comment: 18 pages, To appear in: "Lasers, Clocks and Drag-Free control:
Exploration of Relativistic Gravity in Space", Springer Series on
Astrophysics and Space Science Library, vol 349, p 15