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This Concept Map, created with IHMC CmapTools, has information related to: Astrophysics and TGD.cmap, ASTROPHYSICS AND TGD 4. Could astrophysical systems be quan- tum coherent? a) The work of Laurent Nottale raised the question whether planetary orbital radii could be understood as Bohr ra- dii with gigantic value of Planck con- stant h_gr= GM_1M_2/v_0, v_0/c≈ 2^(-11): for 3 inner planets v_0 has same order of magnitude as planetary orbital velocity from Bohr rules which are same as for hydrogen atom. For outer pla- nets the value of v_0 is 5 times smal- ler. b) The identification of h_gr as h_eff is excluded since h_gr has gigantic va- lue and Compton lengths of particles with this value of Planck constant would be enormous: Schwartschild radius of Sun multiplied by the mass of planet using the mass of the particle as unit! c) If the notion of h_gr makes sense it must have some other origin and I Ihave made a proposal to this direction. By Equivalence Principle one can apply the Bohr rules equally well to individual particles to get same spectrum of orbital radii. Now the value of h_gr would be much smaller and the dark Compton length would be about GM_1/v_0, roughly 1000 times the Schwartschild radius r_S≈3 km of Sun. Solar radius is about 2.3×10^2 longer. d) For inner planets Compton length would be about 3000 km and roughly .2*10^(-5) times smaller the distance of Earth from Sun. One could interpret this in terms of ordinary dark matter resi- ding at magnetic flux tubes emerging from Sun. What is interesting that the Compton length would be same for all particles of dark matter. e) This raises the question whether macroscopic quantum coherence might pre- vail for dark matter in astrophysical length scales. Could the M^4 projections of partonic 2-surfaces have astrophysi- cal size and could dark matter at them as macroscopic quantum phases be respon- sible for Bohr rules. The ordinary mat- ter would condense around dark matter de-localized along the Bohr orbits., ASTROPHYSICS AND TGD 3. Attempts to model astrophysi- cal system in terms of extre- mals of Kähler action. a) The existing models for astro- physical systems date back to the time when the understand- ing of the relationship between TGD and GRT had not yet de- veloped to the recent level. Hence the models are more like exercises in sub-manifold geometry with physical inter- pretation. Some of the exam- ples considered were following. b) Schwartschild and Reissner- Nordström metrics allowing im- bedding as vacuum extremal. c) The attempt to imbedding R-N type metric as non-vacu- um extremal to M^xS^2, S^2 geodes-ic sphere, suggested difficulties with EP if gravita- tional mass is calculated as the Kähler energy of the so- lution. Cutoff is however nee- ded so that the result was not convincing. d) Model for the final state of the star. A non-vacuum ex- tremal was considered and an approximate solution with 2-D CP_2 projection belonging to homologically non-trivial geo- desic sphere was considered. The basic prediction was the presence of dynamo like struc- ture and the concentration of the mass density at the surfa- ce of the object. e) These models suggest that GRT limit of TGD in terms of effective metric is needed at at least when the the astro- physical object does does not not allow model in terms of vacuum extremal. TGD would be "microscopic" description replacing GRT as an effective theory of gravitation., ASTROPHYSICS AND TGD 1. Under what assumpt- tions extremals of Käh- ler action could pro- vide sensible models for astrophysical sys- tems? a) The original approach started with guesses for the extremals of Kähler action which might be applied to a modelling of astrophysical objects li- ke stars and galaxies. b) The basic problem was was whether GRT follows from TGD or not. The general solutions of Ein- stein's equations are cer- tainly not imbeddable to M^4xCP_2 and it has be- come clear that GRT spa- cetime is only effective notion. Its metric is ob- tained by summing gravi- tational effects of various space-time sheets on test test particle having topo- logical sum contacts to all these space-time sheets. c) The challenge is there- fore to understand whet- hter single preferred ex- tremal could provide a re- alistic description of an astrophysical object un- der some circumstances. d) One might guess that this could be case under highly symmetric situa- tions when the number of space-time sheets in- volved is smaller or their effects sum up to some- thing very simple. Ein- stein's equations would of course be satisfied by the extremal., ASTROPHYSICS AND TGD 2. Maxwell-Einstein action as a model for effective space-times. a) Vacuum extremals of Kähler action are the most obvious candidates in this respect. b) Einstein-Maxwell action is expected to be a natural guess for the variational principle determining effec- space-time surface. c) In TGD framework Eu- clidian space-time regions gions represent lines of generalized Feynman dia- grams and a very natural question is whether black hole interiors might be re- placed by them. A deform- ation making the radial component of Schwartshild metric finite at horizon ma- kes it light-like surface at which the determinant of four-metric vanishes just as it does at wormhole throats at which induced metric changes its signa- ture. This would suggest that Euclidian regions in- deed provide a proper description of black-hole interiors. d) Einstein-Maxwell action allows Reissner-Nordström solution as Minkowskian metric and CP_2 as an Eu- clidian metric with cosmolo- gical constantl, which is lar- ge and characterizes CP_2 size. S-N solution is repre- sentable as vacuum extre- mal and CP_2 type vacuum extremals correspond to CP_2 as gravitational instanton.
