  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.
