Mathematics – Logic
Scientific paper
May 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008gregr..40.1071b&link_type=abstract
General Relativity and Gravitation, Volume 40, Issue 5, pp.1071-1086
Mathematics
Logic
Relativity, Differential Topology
Scientific paper
In their origins Einstein’s studies of relativity principles called into question the validity of important assumptions that had previously been made in formulating physical theories, assumptions made without investigation into alternatives. Examples of this include notions of absolute time and space, flat Euclidean geometry, and trivial topology. In this paper, we review an intermediate niche, differentiable (smooth) structure, which must be defined between topology and geometry. We now know that this choice need not be trivial. Just as it seemed for centuries to be obvious that space should be flat, so it would seem until recently that standard, trivial, smoothness for spacetime is the only choice. We now know that this is not true. In this paper we review these topics in the light of very surprising and often counter-intuitive mathematical discoveries of the last 20 years or so. Since our regions of observability are necessarily constrained we do not have any a priori justification for extending standard smoothness globally. This opens up the possibility of non-standard extension of solutions to field equations to exotically smooth regions, leading to examples such as exotic black holes and exotic cosmological models.
No associations
LandOfFree
New level of relativity 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 New level of relativity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New level of relativity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1541304