Rotating Curzon-Chazy metric

TL;DR

This paper analyzes the properties of the rotating Curzon-Chazy metric, revealing a singular horizon, multiply connected spatial hypersurfaces, and potential causality violations that could relate to tachyonic phenomena.

Contribution

It introduces a detailed study of the rotating Curzon-Chazy metric, highlighting its singular horizon, complex topology, and implications for causality and high-energy physics.

Findings

Singular event horizon with infinite area.

Multiply connected spatial hypersurfaces.

Potential causality violations allowing superluminal speeds.

Abstract

We demonstrate that the Curzon metric for a positive mass configuration possesses a singular event horizon with infinite area. This singularity has significant implications, revealing that the three-dimensional spatial hypersurfaces, which are orthogonal to the Killing vector field, exhibit a multiply connected structure. Furthermore, we investigate the dynamics of a test particle orbiting a central $\gamma$-object within this spacetime. It is found that under certain conditions, the particle's velocity can approach the speed of light, leading to an exceptionally high total energy at a specific value of the deformation parameter governing the spacetime structure. Moreover, we uncover a causality issue for a critical value of the deformation parameter, where the test particle can exceed the speed of light, potentially offering new insights into the theoretical existence of tachyons. This study contributes to the understanding of relativistic objects in deformed spacetimes and suggests that such violations of causality could play a role in explaining the elusive nature of tachyonic phenomena in high-energy physics.