Local criteria for the existence of an accelerated frame of reference

TL;DR

This paper establishes a local criterion for the existence of accelerated frames, showing they can exist where a non-isotropic vector field remains non-degenerate, providing a new geometric condition in relativity.

Contribution

It introduces a novel local criterion based on vector field degeneracy for the existence of accelerated frames in spacetime.

Findings

Accelerated frames exist where the vector field remains non-isotropic.

The criterion links the existence of accelerated frames to the degeneracy of vector fields.

Provides a geometric condition for accelerated frame existence in relativity.

Abstract

A local criteria for the existence of an accelerated frame of reference is found. An accelerated frame of reference could exist in all regions where a non-null (non-isotropic) vector field does not degenerate in a null (isotropic) vector field.