On 10/20/2013 6:03 AM, Henry Baker wrote:
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?
The orbital period is the obvious measure, but they could also measure the deflection of light passing near the Sun. Brent Meeker
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