Prof. Mikołaj Korzyński (Center for Theoretical Physics, PAS): Redshift drift, position drift and caustics in general relativity

This talk will be based on a graduate course I delivered at the Astrophysical Relativity School in Chęciny 2023 and should be accessible for anyone with a bit of relativity background. I will discuss the redshift and the position drifts in general relativity, i.e. the temporal variations of the redshift and the position on the sky of a light source, as registered by an arbitrary observer. I will present the derivation of exact relativistic formulas for the drifts, in which they are expressed in terms of the kinematic variables characterizing the motions of the source and the observer, i.e. their momentary 4-velocities and 4-accelerations, as well as the spacetime curvature along the line of sight. The formulas we derive are completely general and involve automatically all possible GR effects. They may be regarded as the counterpart of the Sachs optical equations for temporal variations of the standard observables. I will discuss their physical consequences, especially interesting in spacetimes with caustics, and their possible applications to the gravitational lensing theory, astrometry and cosmology.

‍Warsaw colloquium for theoretical physics at CTP PAS – 2024-06-19