Timeline for Floer homology and Invariants for Einstein Field Equations?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 23, 2012 at 19:52 | comment | added | Kelly Davis | The Hilbert-Palatini formulation of GR is first order. So, if one really wants to take this path, which I think is likely the wrong road to go down, one should study the Hilbert-Palatini formulation. However, I think the real problem is that GR instantons, as Witten mentions in "Global gravitational anomalies", should be thought of as exotic four-manifolds not as global minima of the Hilbert-Palatini action. | |
| Aug 23, 2012 at 18:49 | comment | added | Robert Haslhofer | one more clarification: the suggestion "absolute minima of the Einstein-Hilbert functional" doesn't work, since the second variation of this functional has opposite signs in conformal and TT directions (this is of course very much related to the fact that the linearization of the Einstein tensor is not elliptic). However, for the Perelman functional there are extrema, e.g. (with Perelman's sign convention) a flat metric on a torus or a Ricci-flat metric on a K3 surface are absolute maxima. | |
| Aug 23, 2012 at 17:45 | comment | added | Liviu Nicolaescu | @Deane You are right. | |
| Aug 23, 2012 at 15:48 | comment | added | Deane Yang | Just a clarification. The original Yang-Mills equations, i.e. the Euler-Lagrange equations for the curvature functional, are in fact second order. But what happens is that there are first order equations, curvature is self-dual, that imply the Yang-Mills equations, and these equations are a lot easier to study than the second order ones. But you're right that there seems to be no analogous first order system for Einstein's equations. | |
| Aug 23, 2012 at 8:32 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |