On the Ricci Curvature of Compact Spacelike Hypersurfaces in Einstein Conformally Stationary-Closed Spacetimes

Details On the Ricci Curvature of Compact Spacelike Hypersurfaces in Einstein Conformally Stationary-Closed Spacetimes On the Ricci Curvature of Compact Spacelike Hypersurfaces in Einstein Conformally Stationary-Closed Spacetimes

Apr 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003gregr..35..651a&link_type=abstract

General Relativity and Gravitation, v. 35, Issue 4, p. 651-665 (2003).

Computer Science

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In this paper we develop an integral formula involving the Ricci and scalar curvatures of a compact spacelike hypersurface M in a spacetime \overline{M} equipped with a timelike closed conformal vector field K (in short, conformally stationary-closed spacetime), and we apply it, when \overline{M} is Einstein, in order to establish sufficient conditions for M to be a leaf of the foliation determined by K and to obtain some non-existence results. We also get some interesting consequences for the particular case when \overline{M} is a generalized Robertson-Walker spacetime.

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