Relativistic Top Deviation Equation and Gravitational Waves

TL;DR

This paper derives a generalized relativistic top deviation equation from top theory, extending the geodesic deviation equation, to potentially enhance gravitational wave detection methods, especially for inflationary waves via cosmic background polarization.

Contribution

It introduces a new relativistic top deviation equation that generalizes the geodesic deviation equation for spinning particles, aiding gravitational wave research.

Findings

Derived a relativistic top deviation equation from top theory.

Showed the equation reduces to the geodesic deviation for spinless particles.

Proposed application in detecting inflationary gravitational waves.

Abstract

By using the relativistic top theory, we derive a relativistic top deviation equation. This equation turns out to be a generalization of the geodesic deviation equation for a pair of nearby point particles. In fact, we show that when the spin angular momentum tensor associated to the top vanishes, such a relativistic top deviation equation reduces to the geodesic deviation equation for spinless point particles. Just as the geodesic deviation equation for spinless particles can be used to investigate the detection of gravitational waves, our generalized formula for a relativistic top can be used to study the gravitational wave background. Our formulation may be of special interest to detect the inflationary gravitational waves via the polarization of the cosmic background radiation.