Is there not a theorem about direction fields on a sphere such that there
must be at least one (or is it two) singularities. This has been
popularized by means of an analogy (that isn't quite perfect) about hair
on our heads. One concludes that we must have a part (or something like
one). Now, could Hawking be referring to a topological property of black
holes such that the original theorem about direction fields (as in ODEs)
doesn't apply there or doesn't mean what it usually means elsewhere OR is
it a mishearing or a typo. Only trying to help, but I'm afraid this may
not. Certainly, it would help to have the context and the preceding and
following remarks.