R P A C Newman 1987 Class. Quantum Grav. 4 277 doi:10.1088/0264-9381/4/2/011
R P A C Newman
Show affiliationsA marginal 2-surface is, by definition, covered by a 2-surface admitting a nowhere-zero null normal field of zero expansion. A complete marginal 2-surface which is either compact, or non-compact and subject to certain asymptotic geometric constraints, is said to be well tempered. A well tempered marginal 2-surface admitting a nowhere-timelike variation through well tempered marginal 2-surfaces is said to be stable. In a spacetime satisfying the dominant energy condition, a stable well tempered marginal 2-surface is homeomorphic to S2, P2, R2, T2, S*R a Klein bottle or a Mobius band. Only the topologies S2, P2 and R2 may be compatible with genericity conditions. Of stable compact embedded marginal 2-surfaces which are bounding in a spacelike hypersurface, those homeomorphic to P2 occur in pairs, as do those homeomorphic to a Klein bottle. Stable compact embedded marginal 2-surfaces which are achronal and develop from data on a simply connected partial Cauchy surface are homeomorphic to S2 or T2.
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds (See also 22E65, 57S05)
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
Issue 2 (March 1987)
R P A C Newman 1987 Class. Quantum Grav. 4 277
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