Re: No Hair

["Paul Camp" <pjcamp@coastal.edu>]

There is such a theorem. There must always be at least one coordinate 
singularity on a sphere (e.g. at the north and south poles, longitude 
is undefined). This is not to my knowledge directly relevant to the 
no-hair claims for black holes but it is quite relevant for another 
area of general relativity that Hawking was involved in, namely the 
singularity theorems that pop up in cosmology. The upshot was that 
singularities are general features of all cosmological models 
satisfying some very weak general assumptions. It had been suspected 
previously that they might have been artificial features of cosmology 
following from simplifiying symmetry assumptions that may not be 
exactly valid. Hawking, Ellis and others showed that so long as 
gravity is treated according to classical general relativity, you get 
singularities pretty much.

> 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.

Paul J. Camp                   "The Beauty of the Universe
Assistant Professor of Physics  consists not only of unity
Coastal Carolina University     in variety but also of 
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pjcamp@coastal.edu                    --Umberto Eco
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