(Submitted August 08, 1997)
What is the volume of a black hole?
Our intuitive sense of volume breaks down in the strong gravitational
region in a black hole. So while the "size" of a black hole is given
by the radius of its event horizon, it's volume is not determined by
the usual 4/3*pi*r3. Instead, relativity makes it more complicated
than that. As you pass the event horizon, the spatial direction 'inwards'
becomes 'towards the future'-- you WILL reach the center, it's as
inevitable as next Monday. The direction outsiders think of as their
future becomes a spatial dimension once you are inside. The volume of
a black hole, therefore, is its surface area times the length of time
the hole exists (using the speed of light to convert from seconds to meters).
Since a black hole last practically forever, the black hole's volume is
almost infinite. (This is also a way of explaining the fact that you can
pour stuff into a black hole forever and never fill it up. Another reason
why black holes never fill up is that the radius of the event horizon
increases as the mass of the black hole increases.)
David Palmer and Jim Lochner
for Ask an Astrophysicist