Are rigid non-inertial frames of reference really rigid?

TL;DR

This paper critically examines the concept of rigidity in non-inertial frames within special relativity, revealing that different definitions of rigidity are not equivalent and that M"oller rigid frames are only locally rigid, not globally.

Contribution

It introduces multiple definitions of rigidity in non-inertial frames and analyzes their differences through examples, clarifying the physical implications and the non-Euclidean geometry involved.

Findings

Different rigidity definitions are not equivalent.

M"oller rigid frames are locally but not globally rigid.

Non-Euclidean geometry influences non-inertial frame properties.

Abstract

In this paper the notion of the rigid frame of reference within special relativity is analysed. Three definitions of rigidity are formulated. By using several examples of non-inertial frames, it is shown that these definitions are not equivalent. It is also shown that so called M\"oller rigid non-inertial frames are locally rigid, but do not exhibit global rigidity. The physical meaning of this phenomenon is discussed, as well as its relation to the non-Euclidean nature of space in non-inertial frames of reference. (russian version)