tag:blogger.com,1999:blog-8666091.post112933004596292433..comments2021-05-03T21:54:48.969+02:00Comments on The Reference Frame: Geometric transitionsLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8666091.post-21814113945077210702012-08-04T16:47:49.653+02:002012-08-04T16:47:49.653+02:00Dear Bárbara, thanks for your kind words.
1) One...Dear Bárbara, thanks for your kind words.<br /><br /><br />1) One may slice a finite neighborhood of the tip of the cone along the values of "distance from the tip", and the slices will be S2 x S3 up to some distance. Later, however, the "result of the manifold", whatever it is, will show up. It can have a complicated topology and not every singular manifold with a conifold singularity may be globally sliced to S2 x S3 slices, of course.<br /><br /><br />2) Sorry, I don't understand this question at all. In general, you can't just replace pieces of geometry by something completely different. Geometry has to obey stringent conditions, essentially Einstein's equations (Ricci flatness) so while I am not sure what you exactly wanted to replace by what and why, I guess that it is not possible.<br /><br /><br />3) One may easily prove that the conifold singularity isn't just a coordinate singularity. The Riemann tensor clearly goes to infinity. That's true for all cones that are not locally flat (the curvature radius is equal to the distance from the tip of the cone times a universal constant) and the S2 x S3 -based conifold is obviously not Riemann-flat.<br /><br /><br />Otherwise I don't want to "remove it" at any cost. String theory really makes it possible for spacetime to be a conifold - it allows well-defined predictions even at this geometry that naively looks singular, from the viewpoint of "just the geometry", so classical GR would be ill-defined but string theory is OK on this space.<br /><br /><br />All the best<br />LMLuboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-65006401237303577762012-08-04T15:41:16.858+02:002012-08-04T15:41:16.858+02:00Hello, thank you very much for your simple words t...Hello, thank you very much for your simple words to explain something complex, I have some questions:<br /> <br /> 1) Ok, the base of the cone is S^2xS^3 but as we move away from the singularity it remains S^2xS^3 ?<br /> <br /> 2) Change the smooth peak for something does not affect the reality of things, i.e the physics of what this happening? <br /> <br />3) Why do you want to remove the singularity, apart from the fact that I want to be Calabi Yau Non compact, Ricci flat and Kahler, what is the benefit of removing the singularity? If the singularity is a coordinate and not only physical?<br /> <br />thanks for replying, all the best :-)Bárbara Yaeggyhttp://www.facebook.com/barbara.yaeggynoreply@blogger.com