Show that time stands still at the Schwarzschild radius of a black hole. Specifically, demonstrate that Dt_f → ∞ when d = d_S in the time dilation equation for any value of Dt_d. The implications of this result are clear: As one nears the Schwarzschild radius of a black hole, gravitational time dilation stretches the interval between successive ticks on the clock as seen by a distant observer until they become infinitely long, effectively freezing the motion just as the Schwarzschild boundary is crossed. This essentially prevents the distant observer from ever obtaining any information about conditions inside the black hole.