It’s rare that a new discovery can stop an astrophysicist in their tracks and leave them lost for words. We’re used to media hype around results that are not really all that big a deal, and usually, by the time something hits the news, it’s already been digested (and often dismissed) by the astrophysics community. The BICEP2 detection of primordial gravitational waves, though -- that was different. It completely rewrote the agenda for every journal club, group meeting, hallway conversation, and seminar series for a week.
Gravity does indeed wave, I know because the L1 Lagrange points stay with us when we orbit the Sun. Unless you believe that gravity travels faster than light, you have no choice but to call these waves.
The reason physicists hesitate to call this wave motion is because they have the complete sequence, they know the start and end. Simply because physicists cannot locate the complete sequence all the time does not make a new theory of physics, it just makes their equations approximate. But that's OK, just watch your Taylor series expansions, when they don't converge uniformly then pull out the Einstein correction table and make a small adjustment.
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