Expert: Philip Stahl - 9/3/2009

Question
Why do we call Black Holes... "Black Holes?" Don't they exist in three dimensions. Wouldn't it be more accurate to call them "Black Spheres?"

Answer
Hello,

I think that the unfortunate belief that black holes are "spheres" got started with one of Stephen Hawking's black hole "theorems" in the early 70s. According to the main theorem, as I recall (which applied to any *stationary* black hole), a stationary black hole must have a horizon with a *spherical topology* - and it must be either static (zero angular momentum) or axially symmetric or both.

Of course, most *real* holes will not have such conditions applicable, especially the one about being "static". Thus, other geometries than Hawking's enter. For instance, it can be shown that the applicable solution for a Kerr black hole (based on Kerr solution, Kerr-Newman geometry) allows for a spinning *disk* with an infinite density of matter. Thus, the Kerr solution confers a rotating *disk* geometry on the associated region of spacetime.

At this point, let me point out whole vast technical monographs have been written about the assorted black hole geometries, their physical conditions, and various theorems proposed. (Among the most famous of these is "a black hole has no hair", i.e. its final state is determined by its mass (M), charge (Q) and intrinsic angular momentum (S) - with no other independent attributes (the "hair").)

Thus, to give a simplified answer to a question about one type of geometry almost borders on hubris. To do so entails ignoring all sorts of complex aspects (especially mathematical, to do with spacetime topology ) and making a host of simplifying assumptions. (Among which is to avoid the detailed possible relationships between a hole's event horizon, its static limit, and ergosphere).


Basically then, here are the points to be made:

1) When the term "Schwarzschild radius" is used (to describe an object that has or might collapse to a black hole) that is not intended to imply a *spherical* object of some defined radius (applicable to a spherical geometry) is formed, but rather a *gravitational radius*.

That is to say, it's intended to signal or denote a surface of *infinite redshift* - or yielding infinite time between clock ticks. This infinite redshift surface is what we mean by 'the static limit'. Another way to put this is that any light signals exhibit infinite curvature and so can never escape. Hence the name "black hole"

2) The region between the outer "surface" of the infinite redshift and the outer (event) horizon, is called the ergosphere. Again, the name should not be interpreted automatically as denoting an actual spherical shape. (And besides, there are certain geometries for which the static limit and event horizon coincides- hence no ergosphere technically exists.)

3) The black hole is a region of spacetime for which the exact details of the shape of spacetime are foreclosed to us. Calling it a "hole" in 9999 out of 10000 cases, makes much more sense than calling it a "sphere" - black or other.

For now we can only speculate on the nature of holes using recondite mathematics and esoteric spacetime diagrams, most of which ...alas,....are too arcane to be treated in any simplified manner. Or dare I say it, understandable manner!