The kinematics of particles moving in rainbow spacetime

TL;DR

This paper investigates the motion of particles in rainbow spacetime, deriving geodesics for massive particles considering their energy influence, and discusses implications for the Unruh effect.

Contribution

It provides the first derivation of geodesics for particles in rainbow flat spacetime accounting for their energy effects.

Findings

Particle trajectories remain straight lines in rainbow flat spacetime.

The study offers insights into the Unruh effect within rainbow spacetime.

Geodesic equations are explicitly derived for massive particles.

Abstract

The kinematics of particles moving in rainbow spacetime is studied in this paper. In particular the geodesics of a massive particle in rainbow flat spacetime is obtained when the semi-classical effect of its own energy on the background is taken into account. We show that in general the trajectory of a freely falling particle remains unchanged which is still a straight line as in the flat spacetime. The implication to the Unruh effect in rainbow flat spacetime is also discussed.