IS THERE SUCH A THING AS GRAVITY WAVES?

Maybe the question above does not fully illustrate what Im talking about. I saw on an video about relativity that there was something like a gravity "wave". The example they showed was that if the Sun was instantaneously lifted from the centre of our solar system, then all of the planets would move straight in a tangential path from their orbital path. The question I was wondering was, " When the Sun was lifted, without any explosion, just disappeared, would space-time act like a wave and push the planets. This wave is like a pebble dropped in a pond. Or would this tangential path be instantaneous with the time the Sun disappears?"