Revisiting the Light Cone of the Goedel Universe

TL;DR

This paper analyzes the light cone structure in the Goedel universe, deriving metrics, invariants, and singularities to deepen understanding of its geometric properties.

Contribution

It provides a detailed mathematical analysis of the light cone structure, including invariants and singularities, in the Goedel universe for the first time.

Findings

Derived the intrinsic cone metric.

Calculated rotation coefficients of the ray congruence.

Identified and described focal points and singularities.

Abstract

The structure of a light cone in the Goedel universe is studied. We derive the intrinsic cone metric, calculate the rotation coefficients of the ray congruence forming the cone, determine local differential invariants up to second order, describe the crossover (keel) singularities and give a first discussion of its focal points. Contrary to many rotation coefficients, some inner differential invariants attain simple finite standard values at focal singularities.