Suppose we are inside the Schwarzschild radius of a black hole and throw a ball radially outward. It is said that the ball has no possibility to increase its radial coordinate. It must continuously decrease its radial coordinate and reach finally to the center.
I don't understand why this is so. The metric inside the Schwarzschild radius for radial motion is:
I do understand that the ball must follow timelike world-line, i.e., we must have $ds^2>0$, whatever way the ball moves. And for this to happen it is necessary that $dr\ne0$. But the metric does not appear to put any restriction on whether $dr$ shall be positive or negative, because $dr$ appears there as a squared term.
So why the ball can't move with positive $dr$, i.e, radially outward?