Relativistic Rotation in the Large Radius, Small Angular Velocity Limit

TL;DR

This paper compares two approaches to relativistic rotation in a limit where angular velocity is near zero and radius is very large, concluding that only the non-time-orthogonal approach provides valid predictions.

Contribution

It demonstrates that the non-time-orthogonal analysis approach is the correct method for relativistic rotation in this specific limit, challenging traditional local co-moving Lorentz frame methods.

Findings

Non-time-orthogonal approach aligns with physical expectations.

Traditional local Lorentz frame approach yields inconsistent predictions.

The study clarifies the validity of different relativistic rotation models.

Abstract

Relativistic rotation is considered in the limit of angular velocity approaching zero and radial distance approaching infinity, such that centrifugal acceleration is immeasurably small while tangent velocity remains close to the speed of light. For this case, the predictions of the traditional approach to relativistic rotation using local co-moving Lorentz frames are compared and contrasted with those of the differential geometry based non-time-orthogonal analysis approach. Different predictions by the two approaches imply that only the non-time-orthogonal approach is valid.