Gravitational lensing observables in stationary and axisymmetric solutions in general relativity

TL;DR

This paper studies how rotation-induced relativistic effects in axially symmetric dust systems influence gravitational lensing, revealing potential observational signatures of relativistic rotation in astrophysical contexts.

Contribution

It provides a detailed analysis of light deflection in rotating dust solutions, highlighting the impact of off-diagonal metric components on lensing observables and their detectability.

Findings

Rotational effects modify the light deflection angle.

Off-diagonal metric components act as an effective mass.

Asymmetry in background source images indicates relativistic rotation.

Abstract

We investigate light propagation in self-gravitating systems composed of an axially symmetric, stationary, rotating dust fluid. These configurations are intrinsically relativistic, sustained entirely by their rotation, since no compact or finite dust distribution can exist under the same symmetry conditions in Newtonian gravity. In such systems, rotational effects arise from off-diagonal components of the spacetime metric, which are not negligible compared to their Newtonian counterparts. We analyze how these components affect the deflection angle of light, showing that they can be interpreted as contributing an additional effective mass. Moreover, their presence can, in principle, be detected through the characteristic asymmetry they induce in the images of background sources.