Re: Proof of Singularities

"John (Liberty) Bell" <john.bell@xxxxxxxxxxxxxxxxxx> wrote:
Can anybody point me to the reference for the PROOF, by Penrose (Oxford
mathematician) & Hawking (Cambridge physicist), that singularities are
an inevitable consequence of the mathematical apparatus of Einstein's
Field Equation?

I think the proof you're looking for is the one that, given positive
energy conditions (and maybe some other technical conditions which I
forget), the existence of any trapped surfaces implies that there exists
an inextensible geodesic (which is the mathematical property usually
used for the intuitive notion of a singularity).

This proof is given in proposition 9.2.8 of
@Book{Hawking73a,
author = {Stephen W. Hawking and George F. R. Ellis},
title = {The large scale structure of spacetime},
publisher = {Cambridge University Press},
year = 1973,
address = {Cambridge, England},
isbn = {0-521-09906-4},
}

I'm not sure if this gives references to the original papers. If not,
you might try
@Article{Penrose65,
key = {Penrose65},
author = {Roger Penrose},
title = {Gravitational Collapse and Space-Time Singularities},
journal = {Phys. Rev. Lett.},
year = 1965,
volume = 14,
pages = 57
}
and/or
@Article{Penrose70a,
author = {Roger Penrose and Stephen W. Hawking},
title = {The singularities of gravitational collapse and
cosmology},
journal = {Proc. Roy. Soc. Lond. A},
year = 1970,
volume = 314,
pages = 529
}

ciao,

--
-- "Jonathan Thornburg -- remove -animal to reply" <jthorn@xxxxxxxxxxxxxxxx>
Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
Golm, Germany, "Old Europe" http://www.aei.mpg.de/~jthorn/home.html
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

.

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