Why don't constant motion charges produce waves? I'm a little confused about the origin of electromagnetic waves.
Although I can understand their origin mathematically, I get a little confused about the physical intuition of...

Information transfer is restricted to the speed of light; a local change in a field can only perturb distant regions once a light sphere has reached said regions

This makes perfect sense, but I can't understand then why only accelerating bodies product EM waves, and not any motion which would affect a local field (such as linear, constant motion).
Of course, I realise constant motion is entirely relative and by producing EM waves, I'm suggesting the experience of light entirely subjective. But that's not the case, right?
How then does constant motion not produce EM waves, but also disturb a local field and not violate the speed limit on field propagation?
Also, besides appearing in an entirely separate physical model and mathematical framework, does the origin of gravitational waves (and the lack thereof for constant motion mass) follow a similar explanation?
Any and all input is appreciated!
 A: For any charged particle in uniform motion there is an inertial frame in which that particle is at rest, and vice versa. So if the particle shed energy as EM waves due to uniform motion you would have the odd situation that a motionless particle would also have to shed energy as EM waves. Likewise if a motionless particle doesn't create EM waves then neither can one in a state of uniform motion.
A: One difference that might help you is the following. A moving charge certainly has fields that move along with it, so I understand why you might think it would produce waves. But these fields (the electric field, at least) decay as $1/r^2$, just like the field of a static charge. They also "propagate" at the speed of the charge, because they're following it. But the crucial point is that these fields don't carry energy away, or else the charge would slow down.
If you have a charge at rest and you kick it so it starts moving at constant speed, there will be a ripple in the field that goes away at the speed of light and decays as $1/r$. This wave does carry energy, which is taken from your kick. If you give the same impulse to an uncharged an a charged particle, the uncharged one will move faster as a result of this.
