Incompleteness of timelike submanifolds with nonvanishing second fundamental form.

Details Incompleteness of timelike submanifolds with nonvanishing second fundamental form. Incompleteness of timelike submanifolds with nonvanishing second fundamental form.

Mar 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985gregr..17..293b&link_type=abstract

General Relativity and Gravitation, Volume 17, Issue 3, pp.293-300

Physics

Gravitation Theory:Singularities

Scientific paper

Let M be a properly immersed timelike hypersurface of Minkowski space and assume that M has a strictly positive second fundamental form. If each point of M is of diagonal type and dim M ≥ 3, then the Ricci curvature of M is strictly positive on all (nonzero) nonspace-like vectors. Thus M satisfies both the generic and strong energy conditions and a singularity theorem for M may be established.

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