Gan

According to Einstein's theory, the Earth is following a geodesic through spacetime that's curved due to the proximity of the sun's mass. See: http://oh-math.net/1.php

As far as I know, Einstein didn't actually refer to the sun burning out, but his theory says that if the sun suddenly ceased to exist then there would, in a sense, be a wave. This is because the spacetime curvature that the sun had caused would gradually disappear, beginning at the sun's former location, and spreading outward at the speed of light. The result would be that the Earth would, after about 8 minutes, begin to travel at a tangent to its former orbit. It would not have been pushed, and its momentum would be unchanged, but it would be following a new geodesic.

Regarding light, photons that left the sun during the final 8 minutes of its life would still be arriving at Earth for 8 minutes after it ceased to exist.

http://oh-math.net/1.php
http://www.physicsoftheuniverse.com/topics_relativity_curved.html

"Time is what prevents everything from happening at once" - John Wheeler