Nontrivial small-scale structure of spacetime and consequences for particle propagation
Final Report Abstract
The classical spacetime emerging from a quantum-spacetime phase may have nontrivial structure at extremely small length scales. This nontrivial structure affects, in particular, the propagation of electromagnetic waves with experimental consequences. The question remains as to what the small-scale structure embedded in a flat spacetime really looks like. In the absence of a definitive quantum theory of gravity, progress can only be made by small steps. Still, it is important not to rely on ad hoc phenomenological models, but to look for genuine dynamics. In this project, we have done so by using the standard theory of classical gravity (Einstein’s general relativity) coupled to nonstandard topology. We have managed to find two new exact solutions, a vacuum solution and a nonvacuum solution, both with the same nontrivial topology. This type of solution corresponds to a localized spacetime defect. In addition, we have studied particle propagation near these spacetime defects by finding new analytic solutions of the Klein-Gordon equation for scalar particles (similar results hold for photons). Physically, this type of classical spacetime defect may occur as the end product of a quantumtunneling process. The ultimate quantum theory of gravity must decide whether or not such classical spacetime defects appear in the emergent classical spacetime.
Publications
- “Black-hole solution without curvature singularity,” Mod. Phys. Lett. A 28, 1350136 (2013)
F.R. Klinkhamer
(See online at https://doi.org/10.1142/S0217732313501368) - “A nonsingular spacetime defect,” Phys. Rev. D 89, 084064 (2014)
F.R. Klinkhamer and C. Rahmede
- Comparison of spacetime defects which are homeomorphic but not diffeomorphic
F.R. Klinkhamer and F. Sorba
(See online at https://doi.org/10.1063/1.4900883) - Skyrmion spacetime defect
F.R. Klinkhamer
