Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-12-20
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23 pages, 5 figures, iopart style, important changes in the global hyperbolicity part thanks to M. Sanchez
Scientific paper
Since the first work on exotic smoothness in physics, it was folklore to assume a direct influence of exotic smoothness to quantum gravity. In the second paper, we calculate the "smoothness structure" part of the path integral in quantum gravity for the exotic R^4 as non-compact manifold. We discuss the influence of the "sum over geometries" to the "sum over smoothness structure". There are two types of exotic R^4: large (no smooth embedded 3-sphere) and small (smooth embedded 3-sphere). A large exotic R^4 can be produced by using topologically slice but smoothly non-slice knots whereas a small exotic R^4 is constructed by a 5-dimensional h-cobordism between compact 4-manifolds. The results are applied to the calculation of expectation values, i.e. we discuss the two observables, volume and Wilson loop. Then the appearance of naked singularities is analyzed. By using Mostow rigidity, we obtain a justification of area and volume quantization again. Finally exotic smoothness of the R^4 produces in all cases (small or large) a cosmological constant.
Asselmeyer-Maluga Torsten
Krol Jerzy
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