I've been watching Leonard Susskind's lectures on GR (available on the Internet) & had a question. A non-rotating black hole is completely characterized by its mass & therefore its Schwarzschild radius. A bigger black hole has a bigger Schwarzschild radius, and space in the vicinity of the Schwarzschild radius of a very large black hole is relatively flat. Q: Can a point observer outside the Schwarzschild radius of a black hole tell how big the black hole is by examining the curvature of space very near the observer? I.e., suppose the Sun were a black hole, whose Schwarzschild radius is quite small, so the Earth is very far from this radius. Now consider a Sun' whose mass is, e.g., twice as big as the Sun. Its Schwarzschild radius is bigger than before, but if we are still at 1 AU, would we be able to tell _just from the local curvature_ how much mass is in the center of the solar system? Of course, in order to stay in a "stable" orbit, the Earth would have to speed up to match the new mass in the center, but other than the period of the orbit, is there any way for Earth-bound scientists to measure the mass of the Sun' via curvature of space alone?