Minimal surface analog of Schwartschild solution: two horizons and possible connection LIGO anomaly
The twistor lift of TGD has led to a palace revolution inside TGD and led to an amazing simplification of the vision. The earlier view that vacuum extremals of Kähler action should provide models for simplest solutions of Einstein's equations has been modified. Only the vacuum extremals, which are minimal surfaces are accepted. This leads to an amazingly simple view: Einsteinian gravitation could be replaced at the level of single space-time sheet with theory of minimal surfaces in M4× S2, where S2 is homologically trivial geodesic sphere of CP2 so that the induced Kähler form vanishes. Both static solutions satisfying Laplace equation with gravitational self-coupling and solutions describing topological quantized gauge and gravitational radiation classically are obtained. The solutions can be and actually carry non-vanishing gauge charge which can be however very small.
The obvious question is whether the spherically symmetric minimal surface of this kind with stationary induced metric have the physical properties assigned to Schwarschild and Reissner-Nordstöm metrics. The modification of simple calculations done already at 90's for vacuum extremal imbeddings of these metrics leads to an ansatz which gives rise to Newtonian gravitational potential at far away regions. It has also the analog of Schwartschild horizon at which the roles of time and radial coordinate are changed and also another horizon at which the radial direction transforms back to Euclidian so that this horizons is light-like 3-surface at which metric signature changes to Euclidian. Interestingly, there is a recent report about indications that LIGO blackhole has a layer like structure at horizon.
See the new chapter Can one apply Occam's razor as a general purpose debunking argument to TGD? of "Towards M-matrix" or article with the same title.
For a summary of earlier postings see Latest progress in TGD.