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arXiv · gr-qc/9910034

Morse index and causal continuity. A criterion for topology change in quantum gravity

H. F. Dowker·R. S. Garcia·S. Surya
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Abstract

Studies in 1+1 dimensions suggest that causally discontinuous topology changing spacetimes are suppressed in quantum gravity. Borde and Sorkin have conjectured that causal discontinuities are associated precisely with index 1 or n-1 Morse points in topology changing spacetimes built from Morse functions. We establish a weaker form of this conjecture. Namely, if a Morse function f on a compact cobordism has critical points of index 1 or n-1, then all the Morse geometries associated with f are causally discontinuous, while if f has no critical points of index 1 or n-1, then there exist associated Morse geometries which are causally continuous.

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H. F. Dowker, R. S. Garcia, S. Surya. 1999-10-11. Morse index and causal continuity. A criterion for topology change in quantum gravity. https://doi.org/10.1088/0264-9381%2F17%2F3%2F308

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