Relativistic Kinematics and Stationary Motions

TL;DR

This paper develops a Lorentz covariant framework for relativistic kinematic vectors like jerk and snap, classifies stationary motions in D-dimensional spacetime, and explores applications to branes, heat baths, and black hole free fall.

Contribution

It introduces a new covariant classification of stationary motions and extends the formalism to branes and non-stationary cases, including black hole free fall.

Findings

Defined relativistic jerk, snap, and higher-order kinematic vectors.

Provided a Lorentz covariant classification of stationary motions.

Analyzed motions like constant jerk and black hole free fall from a GEMS perspective.

Abstract

The relativistic jerk, snap and all higher-order kinematical D-vectors are defined for the motion of a massive particle in a D-dimensional Minkowski spacetime. We illustrate the formalism with stationary motions, for which we provide a new, Lorentz covariant, classification. We generalize some cases to branes, explaining the relevance to uniform motion in a heat bath. We also consider some non-stationary motions, including motion with constant proper jerk, and free fall into a black hole as viewed from a GEMS perspective.