Relativistic Top Deviation Equation and 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.

19 pages LaTex, references added

References in corpus (4)

• Detection of Polarization in the Cosmic Microwave Background using DASI
• On the motion of spinning test particles in plane gravitational waves
• Spinning particles in gravitational wave spacetime
• Special Purpose Pulsar Telescope for the Detection of Cosmic Gravitational Waves

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• World-line deviation and spinning particles
• The Raychaudhuri equation for spinning test particles
• The Relative Motion of Membranes
• Charged particles with spin in a gravitational wave and a uniform magnetic field
• Linearized gravity as a gauge theory
• On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse
• Spinning test particles in the spacetime of a global monopole