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

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

1999-10-11

arxiv.org/abs/gr-qc/9910034v1

Class.Quant.Grav. 17 (2000) 697-712

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 20 pages, 3 figures

Scientific paper

10.1088/0264-9381/17/3/308

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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