I have some questions about one of the old elevator/spaceship thought experiments. 1. If I am on a spaceship that is far from any massive bodies and is accelerating upward (from my point of view) uniformly at g, is the spacetime in my ship curved or flat? 2. If a beam of light enters the ship from a hole in one of the walls and is initially moving in a direction parallel to the floor, does its path curve downward? 3. If the path is parabolic, does the horizontal velocity decrease so that the overall speed remains at c? I would appreciate any responses.