SOLUTIONS OF NEWTONIAN GRAVITATIONAL WAVES AND GRAVITATIONAL POYNTING VECTOR

Abstract

Solutions to equations producing Newtonian gravitational waves are being presented. The derivations of these equations emerging directly from the second Newton law and mass conservation applied to a continuous mass distribution, e.g., a compressible fluid or equivalent, have already been shown to lead to a form identical to the Maxwell equations for electromagnetism subject to a specific condition. Consequently, Newtonian gravitational waves are Lorentz invariant when the speed of wave propagation equals the speed of light. The resulting equations can derive a gravitational Poynting vector in complete analogy to the electromagnetic Poynting vector. A stationary solution exists for a spherical mass, creating the gravitational field. The evolution of a gravitational wave emerges and is presented as a linear, neutrally stable solution around this stationary one.