Optical drift effects in general relativity

TL;DR

This paper develops a fully relativistic, covariant framework to compute optical drift effects such as apparent position, redshift, and distance changes of distant objects in arbitrary spacetimes, extending geometric optics formalism.

Contribution

It introduces a hierarchy of ODEs for calculating optical drift effects in general relativity, including non-perturbative relations linking lensing, parallax, and redshift drift.

Findings

Derived relations between lensing and apparent position drift.

Established connection between position drift and redshift drift.

Provided a covariant approach applicable to arbitrary spacetimes.

Abstract

We consider the question of determining the optical drift effects in general relativity, i.e. the rate of change of the apparent position, redshift, Jacobi matrix, angular distance and luminosity distance of a distant object as registered by an observer in an arbitrary spacetime. We present a fully relativistic and covariant approach, in which the problem is reduced to a hierarchy of ODE's solved along the line of sight. The 4-velocities and 4-accelerations of the observer and the emitter and the geometry of the spacetime along the line of sight constitute the input data. We build on the standard relativistic geometric optics formalism and extend it to include the time derivatives of the observables. In the process we obtain two general, non-perturbative relations: the first one between the gravitational lensing, represented by the Jacobi matrix, and the apparent position drift, also called the cosmic parallax, and the second one between the apparent position drift and the redshift drift. The applications of the results include the theoretical study of the drift effects of cosmological origin (so-called real-time cosmology) in numerical or exact Universe models.