|A man falls into the center of the earth — how much does he weight? Which way is space bent in the center of the earth? — JW, Virginia Beach, VA
At the center of the earth, the man would be truly weightless and the space around him would be exactly flat (no curvature due to gravity). This special situation occurs because the gravitational effects of the earth around the man are perfectly balanced. With equal amounts of the earth's mass on each side, there is no special direction in which the man would accelerate.