[Yahya A.Sharif (OP)]

Gravitational waves won't be caused by constant speed of matter.
Matter at constant speed will change its position with respect to space-time, and place itself in new points in space-time, these new points of space-time will cause new curvature of space-time .

This new curvature can't exists at infinity since it starts at a momentat at points where there weren't previous curvature, in fact it will extend with the speed of light c.

All matter after the big bang can't be in a fixed position,So every object has gravity limited to a range extendable with the speed of light c.

If new gravity curvature extending at the speed of light can be detected then this  will be a proof for my assumption.

We have two cases:
An accelerated object causes gravitational waves  and object at constant speed causes gravity  expansions.