Four Dimensional Quantum Topology Changes of Spacetimes

Details Four Dimensional Quantum Topology Changes of Spacetimes Four Dimensional Quantum Topology Changes of Spacetimes

1995-03-16

arxiv.org/abs/gr-qc/9503026v2

J.Math.Phys. 37 (1996) 5611-5626

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages, revtex, 13 figures. The calculation of volume and grammatical errors are corrected

Scientific paper

10.1063/1.531725

We investigate topology changing processes in the WKB approximation of four dimensional quantum cosmology with a negative cosmological constant. As Riemannian manifolds which describe quantum tunnelings of spacetime we consider constant negative curvature solutions of the Einstein equation i.e. hyperbolic geometries. Using four dimensional polytopes, we can explicitly construct hyperbolic manifolds with topologically non-trivial boundaries which describe topology changes. These instanton-like solutions are constructed out of 8-cell's, 16-cell's or 24-cell's and have several points at infinity called cusps. The hyperbolic manifolds are non-compact because of the cusps but have finite volumes. Then we evaluate topology change amplitudes in the WKB approximation in terms of the volumes of these manifolds. We find that the more complicated are the topology changes, the more likely are suppressed.

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