Is there any empirical evidence for the existence of two horizons? There is evidence that the formation of the recently found LIGO blackhole (discussed from TGD view point in is not fully consistent with the GRT based model (see this). There are some indications that LIGO blackhole has a boundary layer such that the gravitational radiation is reflected forth and back between the inner and outer boundaries of the layer. In the proposed model the upper boundary would not be totally reflecting so that gravitational radiation leaks out and gave rise to echoes at times .1 sec, .2 sec, and .3 sec. It is perhaps worth of noticied that time scale .1 sec corresponds to the secondary p-adic time scale of electron (characterized by Mersenne prime M_{127}= 2^{127}-1). If the minimal surface solution indeed has two horizons and a layer like structure between them, one might at least see the trouble of killing the idea that it could give rise to repeated reflections of gravitational radiation.

The proposed model (see this) assumes that the inner horizon is Schwarstchild horizon. TGD would however suggests that the outer horizon is the TGD counterpart of Schwartschild horizon. It could have different radius since it would not be a singularity of g_{rr} (g_{tt}/g_{rr} would be finite at r_{S} which need not be r_{S}=2GM now). At r_{S} the tangent space of the space-time surface would become effectively 2-dimensional: could this be interpreted in terms of strong holography (SH)?

One should understand why it takes rather long time T=.1 seconds for radiation to travel forth and back the distance L= r_{S}-r_{E} between the horizons. The maximal signal velocity is reduced for the light-like geodesics of the space-time surface but the reduction should be rather large for L∼ 20 km (say). The effective light-velocity is measured by the coordinate time Δ t= Δ m^{0}+ h(r_{S})-h(r_{E}) needed to travel the distance from r_{E} to r_{S}. The Minkowski time Δ m^{0}_{-+} would be the from null geodesic property and m^{0}= t+ h(r)

Δ m^{0}_{-+} =Δ t -h(r_{S})+h(r_{E}) ,

Δ t = ∫_{rE}^{rS}(g_{rr}/g_{tt})^{1/2} dr== ∫_{rE}^{rS} dr/c_{#} .

The time needed to travel forth and back does not depend on h and would be given by

Δ m^{0} =2Δ t =2∫_{rE}^{rS}dr/c_{#} .

This time cannot be shorter than the minimal time (r_{S}-r_{E})/c along light-like geodesic of M^{4} since light-like geodesics at space-time surface are in general time-like curves in M^{4}. Since .1 sec corresponds to about 3× 10^{4} km, the average value of c_{#} should be for L= 20 km (just a rough guess) of order c_{#}∼ 2^{-11}c in the interval [r_{E},r_{S}]. As noticed, T=.1 sec is also the secondary p-adic time assignable to electron labelled by the Mersenne prime M_{127}. Since g_{rr} vanishes at r_{E} one has c_{#}→ ∞. c_{#} is finite at r_{S}.

There is an intriguing connection with the notion of gravitational Planck constant. The formula for gravitational Planck constant given by h_{gr}= GMm/v_{0} characterizing the magnetic bodies topologically for mass m topologically condensed at gravitational magnetic flux tube emanating from large mass M. The interpretation of the velocity parameter v_{0} has remained open. Could v_{0} correspond to the average value of c_{#}? For inner planets one has v_{0}≈ 2^{-11} so that the the order of magnitude is same as for the the estimate for c_{#}.

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.

## 1 comment:

Very good.

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