The general field equation for GR is Rab - 1/2 gab R = 8πTab where I am setting G = 1 and c = 1. Also, the vacuum solution is Rab = 0 But it seems to me that this "vacuum" solution must hold even when there is matter present. Pick a point within a planet. Then excavate an infinitesimal vacuum chamber about the point. That can't affect the solution there because the local contribution to the solution is infinitesimal. Therefore, whether there is a vacuum at a point or not makes no difference, the vacuum solution still holds. Rab = 0 is a constraint on curvature that is everywhere satisfied. So why can't the field equation then be simplified to this by replacing Rab with 0? - 1/2 gab R = 8πTab That makes it look a lot like Gauss's law of gravity, which does not add in a zero term representing a vacuum solution. ∇2[itex]\varphi[/itex] = 4πρ This makes more sense to me. The solution is determined by the sources only, not by a zero valued vacuum solution. Did Einstein glue together two equations into one for brevity? If so, why doesn't Gauss's law need another equation? And why would a vacuum solution be needed in addition to the source term in GR?