Sunday, November 12, 2017

general relativity - Exotic differentiable structures in physics


When reading a bit on exotic spheres and exotic $\mathbb{R}^4$'s, I came across some papers of Carl H. Brans and Torsten Asselmeyer-Maluga:




  • "Exotic differentiable structures and general relativity" (1993),


http://arxiv.org/abs/gr-qc/9212003



  • "Exotic Smoothness and Physics" (1994)


http://arxiv.org/abs/gr-qc/9405010



  • "Exotic Smoothness on Spacetime" (1997)



http://arxiv.org/abs/gr-qc/9604048



  • "Smooth quantum gravity: Exotic smoothness and Quantum gravity" (2016)


http://arxiv.org/abs/1601.06436


Without having read the papers, I was wondering:




  • Are these ideas of considering exotic structures "commonly" thought of as useful to pursue?





  • Are there any "significant" results?




These are vague questions, I understand that, but I'm just trying to get an idea on whether bringing these kinds of "deeper" mathematics into the physics is (in this particular case) something worth doing. Of course, if someone knows more and is willing to share, I'm willing to read.




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