My understanding of electromagnetic radiation is this: When a charged particle accelerates, there is a change in its associated electric field at all points in space, though not instantaneously. The "electric field wave" is basically the propagation of the disturbance that occurs when the electric field at a given point in space "updates" due to the acceleration of the particle. And of course, this electric field wave is accompanied by a perpendicularly propagating magnetic field wave, and together they travel at speed of light c. So analogously, any particle that has a non-zero mass must have a gravitational field, and whenever that particle accelerates, there should be a similar gravitational disturbance that radiates (I'm assuming also at the speed of light), right? In other words, is the existence of a gravitational "wave" not undeniable based on these considerations? Therefore I'm wondering what the current debate regarding the "existence" of gravity waves and gravitational radiation is about. They must exist, no? Is it just a question of whether the waves are too weak to be of any significance experimentally?