Null geodesics and gravitational lensing in a nonsingular spacetime

TL;DR

This paper studies null geodesics and gravitational lensing in a nonsingular spacetime, revealing how the nonsingularity parameter affects observable lensing features, especially in strong deflection regimes.

Contribution

It provides new analytical results for gravitational lensing coefficients and observables in nonsingular spacetimes, including black holes and weakly nonsingular backgrounds.

Findings

Nonsingularity parameter q has negligible effect in weak deflection limit.

Relativistic images in weakly nonsingular spacetime have smaller angular position and magnification.

Angular separation of images is larger in weakly nonsingular spacetime compared to nonsingular black holes.

Abstract

In this paper, the null geodesics and gravitational lensing in a nonsingular spacetime are investigated. According to the nature of the null geodesics, the spacetime is divided into several cases. In the weak deflection limit, we find the influence of the nonsingularity parameter $q$ on the positions and magnifications of the images is negligible. In the strong deflection limit, the coefficients and observables for the gravitational lensing in a nonsingular black hole background and a weakly nonsingular spacetime are obtained. Comparing these results, we find that, in a weakly nonsingular spacetime, the relativistic images have smaller angular position and relative magnification, but larger angular separation than that of a nonsingular black hole. These results might offer a way to probe the spacetime nonsingularity parameter and put a bound on it by the astronomical instruments in the near future.