About the TGD counterparts of blackhole entropy and temperature

Gyanprakash Raj asked about the TGD view of blackhole entropy. In particular, does TGD predict blackhole entropy excess predicted by various models of blackhole trying to understand blackhole information paradox?

TGD forces us to give up the standard view of blackholes as systems having mass concentrated at a single point. The QFT limit of TGD replaces the topologically extremely complex space-time surface with a single region of M⁴ made slightly curved.

1. Outside the horizon, the blackhole-like object (BH) would be like an ordinary blackhole. Inside BH the description as a volume filling flux tube spaghetti, giving rise to maximal density, would be more appropriate.
2. For the TGD counterparts of the ordinary blackholes the flux tube would have thickness of nucleus size scale but an entire hierarchy corresponding to predicted hierarchy of hadron physics labelled by ordinary and Gaussian Mersenne primes is highly suggestive (see this). The difference between stars and blackholes would not be so dramatic as in GRT.

In TGD, the formulas for BH entropy predict dramatic results if ordinary Planck constant is replaced by gravitational Planck constant.

1. The standard blackhole entropy is extremely small. It is proportional to 1/ℏ and if ℏ is replaced with its gravitational counterpart ℏ_gr it becomes even smaller.
2. The standard blackhole temperature is proportional to ℏ and increases equally dramatically. The explanation would be gravitational quantum coherence which increases the geometric pixel proportional to Planck length squared and increases the energy scale.

Just for fun one can look for the standard formulas for S_B and T_B in the TGD framework.

Consider first the blackhole entropy.

1. Blackhole entropy S_B is essentially the area A of black hole divided by the area unit l_P² propto ℏG:

   S_B propto A/l_P² .

2. Suppose one replaces ℏ with gravitational Planck constant

   ℏ_gr= GMm/β₀ = r_Sm/2β₀ .

   Here the mass m would be naturally the mass of the nucleon characterizing monopole flux tubes of spaghetti as gravitationally dark giant nuclei.

3. This scales up the l_P² l_P²→(r_sm/2β₀*ℏ)l_P² = (Λ_gr/λ)l_P², where Λ_gr=r_s/2β₀ is mass independent gravitational Compton length (Equivalence Principle). λ is the ordinary Compton length.
4. β₀ is a velocity parameter whose interpretation I have finally understood. TGD is distinguished from GRT in that it allows flat warped space-time surfaces for which light velocity c in M⁴ is reduced to β₀. See (see this) .
5. The black hole entropy is scaled dramatically downwards so that one cannot speak of excess entropy. One could say that the scaling of Compton length to gravitational one increases the size of the pixel defining the bit. The interpretation of small entropy could be in terms of gravitational quantum coherence. A BH-like object would be an extremely ordered quantum coherent system, totally unlike the standard BH. Also the centers of the stars could be these kinds of objects.

What about blackhole temperature?

1. The blackhole temperature is given by T_B= ℏ/(8πr_s) and is extremely low.
2. In the replacement ℏ→ℏ_gr , T_B would be replaced by

   T_B= m/8πβ₀, where m is the nucleon mass.

3. For β₀=1, one one would have T_B ∼ 37.4 MeV. However, the Nottale's Bohr orbit model for planets predicts for the Sun the value β₀ ∼ 2^-11. This would give

   T_B= 79m_p ,

   which is not far from the mass of Z boson 85.7 m_p, which would correspond to M₈₉ hadron physics TGD indeed predicts that solar wind and solar energy production is due to the decay of M₈₉ hadrons (basically nucleons) at the surface of the Sun. The mass of the M₈₉ pion is 512 times that of the ordinary pion and equals 71.7 GeV.

4. Could one think of detecting gamma radiation from the Sun with this energy? Note that the decay of M₈₉ would produce gamma rays with energy 39.5 GeV. There is indeed a mysterious gamma ray emission from the Sun around 40 GeV energy (see this).

   For a summary of earlier postings see Latest progress in TGD.

   For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.