Spatial geometry of the rotating disk and its non-rotating counterpart

TL;DR

This paper provides a general relativistic analysis of rotating disks, revealing hyperbolic geometry for observers on the disk and discussing how clock synchronization affects spatial measurements.

Contribution

It offers a comprehensive relativistic framework for understanding the geometry of rotating disks, addressing conceptual issues present in special relativity.

Findings

Observers on the rotating disk perceive hyperbolic spatial geometry.

Clock synchronization significantly influences spatial measurement interpretations.

The approach simplifies conceptual understanding compared to special relativity.

Abstract

A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry of their proper space is hyperbolic. This has interesting consequences concerning their interpretation of the geometry of a non-rotating disk having the same radius. The influence of clock synchronization on spatial measurements is discussed.