Gravitational Radiation: Maxwell-Heaviside Formulation

Abstract

To fully describe gravitational energy flux by using an analog to the Maxwell-Heaviside equations for electrodynamics, the Liénard–Wiechert potentials and fields are derived for gravitation along with radiation patterns and corresponding Larmor formulas for total radiated power. Due to attraction of like gravitational charges (masses) as opposed to repulsion of like electrical charges, the mass-density and current-density terms pick up a negative sign along with a factor of the universal gravitational constant, G. This results in a sign change of the Poynting vector, indicating energy is gained by the field as opposed to energy being lost by the field, such is the case for electromagnetic radiation. The gravitational and cogravitational fields, analogous to the electric and magnetic fields, respectively, behave as described by Heaviside and Lorentz. Like an electric charge, a gravitic charge (mass) in uniform motion is found to produce a spherical field which contracts along the axis of motion as its velocity approaches the limiting speed of propagation. The speed of gravitational propagation is assumed to be equivalent to that of light, though this may not necessarily be the case. For an accelerated mass, the resulting gravitational radiation mirrors the dipole pattern produced by an accelerated electric charge, similarly oriented about the axis of acceleration yet contracting in the reverse direction at relativistic speeds. These results seek to further inquire on the nature of gravitational fields

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