- Curvature comes from the stress tensor so how can there be curvature when there is no mass?
You're on Earth. You throw a ball and watch its trajectory. It's curved. That's because the Earth is curving space-time at every point along the trajectory. But the Earth itself is not present along the trajectory - there is no matter along the trajectory (let's ignore the air and any radiation that might be present) - so how is it curving the space there? There's not supposed to be action at a distance. Does it have something to do with gravitational waves? If so (and perhaps even if not because I'm still curious), what part of the field equations point to the existence of gravitational waves?