A Borde et al 1999 Class. Quantum Grav. 16 3457 doi:10.1088/0264-9381/16/11/303
Causal continuity in degenerate spacetimes
A Borde
, H F Dowker
, R S Garcia, R D Sorkin§ and S Surya||
A change of spatial topology in a causal, compact spacetime cannot occur when the metric is globally Lorentzian. On any cobordism manifold, however, one can construct from a Morse function f and an auxiliary Riemannian metric hµ
a causal metric gµ which is Lorentzian almost everywhere except that it degenerates to zero at each critical point of f. We investigate causal structure in the neighbourhood of such a degeneracy, when the auxiliary Riemannian metric is taken to be Cartesian flat in appropriate coordinates. For these geometries, we verify the conjecture that causal discontinuity occurs if and only if the Morse index is 1 or n - 1.
- PACS
-
04.20.Gz Spacetime topology, causal structure, spinor structure
- MSC
- Subjects
- Dates
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Issue 11 (November 1999)
Received 3 May 1999
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Causal continuity in degenerate spacetimes
A Borde et al 1999 Class. Quantum Grav. 16 3457
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