LIGO blackhole anomaly and minimal surface model for star

The TGD inspired model of star as a minimal surface with stationary spherically symmetric metric suggests strongly that the analog of blackhole mertric as two horizons. The outer horizon is analogous to Scwartschild horizon in the sense that the roles of time coordinate and radial coordinate change. Radial metric component vanishes at Scwartschild horizon rather than divergence. Below the inner horizon the metric has Eucldian signature.

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 M₁₂₇= 2¹²⁷-1). 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 m⁰+ h(r_S)-h(r_E) needed to travel the distance from r_E to r_S. The Minkowski time Δ m⁰_-+ would be the from null geodesic property and m⁰= t+ h(r)

Δ m⁰_-+ =Δ t -h(r_S)+h(r_E) ,

Δ t = ∫_rE^r_S(g_rr/g_tt)^1/2 dr== ∫_rE^r_S dr/c_# .

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

Δ m⁰ =2Δ t =2∫_rE^r_Sdr/c_# .

This time cannot be shorter than the minimal time (r_S-r_E)/c along light-like geodesic of M⁴ since light-like geodesics at space-time surface are in general time-like curves in M⁴. Since .1 sec corresponds to about 3× 10⁴ km, the average value of c_# should be for L= 20 km (just a rough guess) of order c_#∼ 2^-11c 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 M₁₂₇. 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/v₀ 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 v₀ has remained open. Could v₀ correspond to the average value of c_#? For inner planets one has v₀≈ 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.

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