The Covariant Force and Dipole Gravitational Radiation of a Relativistic Particle

The covariant linearized tensor field and force equations of general relativity are transformed into a form identical to the vector equations of electromagnetism and are benchmarked to known solutions. These transformed equations of weak gravitational fields suggest that dipole gravitational radiation, as yet undetected, is a second-order nonlinear product of asymmetric radiation by all bound and unbound quadrupoles. Associated with these dipole gravitational waves is a particle that has the same spin and polarization vectors as a photon, rather than the spin and polarization tensors of a graviton. The covariant equations are benchmarked to the known solutions of: Unbound orbits in a Schwarzschild field; Hilbert repulsion; and a spherical mass in uniform motion. The transformed equations can be used: To apply many aspects of electromagnetism theory and electrodynamics to weak-field gravitation; to design new classes of laboratory tests of general relativity at high speeds, including tests of general relativity at ultrarelativistic speeds at the Large Hadron Collider; and to help characterize more accurately the coalescence of black holes and other compact binaries at gravitational wave observatories, like the Laser Interferometer Gravitational-Wave Observatory.