Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions

Details Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions

1999-03-23

arxiv.org/abs/gr-qc/9903086v2

Class.Quant.Grav. 16 (1999) 2447-2469

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

AmsTex, 23 pages 5 eps figures; replaced figures with ones which are hopefully viewable in pdf format

Scientific paper

10.1088/0264-9381/16/7/319

It is well known that in four or more dimensions, there exist exotic manifolds; manifolds that are homeomorphic but not diffeomorphic to each other. More precisely, exotic manifolds are the same topological manifold but have inequivalent differentiable structures. This situation is in contrast to the uniqueness of the differentiable structure on topological manifolds in one, two and three dimensions. As exotic manifolds are not diffeomorphic, one can argue that quantum amplitudes for gravity formulated as functional integrals should include a sum over not only physically distinct geometries and topologies but also inequivalent differentiable structures. But can the inclusion of exotic manifolds in such sums make a significant contribution to these quantum amplitudes? This paper will demonstrate that it will. Simply connected exotic Einstein manifolds with positive curvature exist in seven dimensions. Their metrics are found numerically; they are shown to have volumes of the same order of magnitude. Their contribution to the semiclassical evaluation of the partition function for Euclidean quantum gravity in seven dimensions is evaluated and found to be nontrivial. Consequently, inequivalent differentiable structures should be included in the formulation of sums over histories for quantum gravity.

Affiliated with

Also associated with

No associations

Rating

Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-431975