Smooth deformation of a Lorentzian manifold and singularities

[MeJennifer]

How can a smooth deformation of a Lorentzian manifold possibly create one or more singularities?

 

[coalquay404]

How can a smooth deformation of a Lorentzian manifold possibly create one or more singularities?

Schoen and Yau solved this problem over two decades ago in the context of asymptotically flat initial data in the last of their three famous papers on the positivity of mass in general relativity. The reference is


@ARTICLE{1983CMaPh..90..575S,
author = {{Schoen}, R. and {Yau}, S.-T.},
title = "{The existence of a black hole due to condensation of matter}",
journal = {Communications in Mathematical Physics},
year = 1983,
month = dec,
volume = 90,
pages = {575-579},
adsurl = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1983CMaPh..90..575S&db_key=PHY},
adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System}
}


Beware, the paper is hugely technical. I can come up with a broad outline of their thinking if you want, but it's still going to be hard to understand.

 

[quantum123]

Just pinch one point and lift it up to infinity.