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I'm teaching a course on black holes this semester using
the new excellent new intro text by Taylor and Wheeler
("Exploring Black Holes"). One of the exercises involves
calculating the local acceleration of gravity for someone
standing on a shell of reduced circumference R surrounding
a nonspinning, spherical black hole of mass M. The answer
turns out to be
g = (M/R^2) / sqrt(1 - 2M/R)