  It is well-known that the Riemann curvature tensor has no discontinuity at
the black hole horizon. It is also well-known that a freely falling observer
takes finite time to reach the horizon from an outside point. However, the
usual assumption is that such an observer resides in a frame of reference
(spaceship) of infinitesimal size. This assumption is justified as long as the
coordinates are continuous enough to assume that the observer's frame is small
compared to the variations of the metric from a local flat metric. Such an
assumption may be invalid when the coordinate system has not only a
discontinuity but a singularity like the one at the horizon. Hence, here, the
characteristics of a finite frame (a spaceship) near a black hole horizon is
discussed. It is shown that clocks placed at the front and rear ends have
different time scales even in the limit when they reach the horizon at the same
time. This renders such a frame physically meaningless. It is also argued that
the forces that are expected to keep a realistic frame (like a spaceship) in
one piece tend to zero near the horizon. So, a physical spaceship is expected
to fall apart near the horizon.
