Nongeodesic motion of spinless particles in the teleparallel gravitational wave background

TL;DR

This paper investigates how spinless particles move in teleparallel gravitational wave backgrounds, revealing nongeodesic motion influenced by torsion, with potential observable effects detectable by GW LISA.

Contribution

It demonstrates that nongeodesic motion of spinless particles occurs in torsionic backgrounds when Cartan contortion is not totally skew-symmetric, and connects torsion effects with gravitational wave observations.

Findings

Contortion obeys a tensor wave constraint.

Damping effects of contortion on particle motion are identified.

Phase difference of π/2 between contortion and gravitational waves.

Abstract

The motion of spinless particles in Riemann-Cartan (RC) $U_{4}$ and teleparallel spacetimes is revisited on the light of gravitational waves hitting on the spinless test particles. It is shown that in the case Cartan contortion is totally skew-symmetric the spinless particles follow geodesics but if this symmetry is dropped they are able to follow nongeodesic worldlines in torsionic background. The case of totally skew contortion and spinning particles may appear either in $T_{4}$ or $U_{4}$ spacetimes. We consider $T_{4}$ nongeodesic motion of spinless test particles in the field of gravitational waves (GW). It is shown that the general contortion obeys a tensor wave constraint and the analysis of a ring of spinless test particles as in General Relativity (GR) hit by the GW leads to damping contortion effects on the nongeodesic motion is undertaken. It is also shown that the contortion and gravitational waves possess a difference of phase of $\frac{\pi}{2}$ and a contortion at the surface of the Earth of $10^{-24} s^{-1}$ computed by Nitsch in the realm of teleparallelism is used to obtain a deviation of the lenght of the separation of test spinless particles compatible with the GR result. To obtain this result data from GW LISA detector is used.