Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods

TL;DR

This paper investigates the gravitational lensing and shadow phenomena in the toron solution of Einstein's equations, combining numerical and analytical methods to compare its properties with known spacetimes like Schwarzschild, Kerr, and NUT.

Contribution

It introduces a detailed analysis of the toron solution's physical properties using ray tracing, highlighting its similarities and differences with established spacetime models.

Findings

The toron solution exhibits unique lensing features due to its NUT parameter.

Ray tracing reveals distinctive shadow structures compared to Schwarzschild and Kerr.

Comparative analysis clarifies the role of the NUT parameter in gravitational phenomena.

Abstract

We present a numerical and analytical study of the so-called `toron' solution of the stationary axisymmetric Einstein equations in vacuum expressed in terms of elliptic functions. The asymptotic behavior of this solution coincides with the one of the NUT solution, i.e., it has a `gravimagnetic' mass known as the NUT parameter while the ordinary mass vanishes. The physical properties of this spacetime are studied via ray tracing. The results are compared to known geodesic flows in Schwarzschild, Kerr and NUT spacetimes to discuss similarities and differences, with a particular emphasis on the comparison of NUT and toron spacetimes.