Super-canonical black-holes are dark matter in the sense that they have no electro-weak interactions and they could have Planck constant larger than the ordinary one so that the value of αs=αK=1/4 is reduced. The condition that αK has the same value for the super-canonical phase as it has for ordinary gauge boson space-time sheets gives hbar=26×hbar0. With this assumption the size of the baryonic super-canonical blacholes would be 46 fm, the size of a big nucleus, and would define the fundamental length scale of nuclear physics.
1. RHIC and super-canonical blackholes
In high energy collisions of nuclei at RHIC the formation of super-canonical blackholes via the fusion of nucleonic space-time sheets would give rise to what has been christened a color glass condensate. Baryonic super-canonical blackholes of M107 hadron physics would have mass 934.2 MeV, very near to proton mass. The mass of their M89 counterparts would be 512 times higher, about 478 GeV. The "ionization energy" for Pomeron, the structure formed by valence quarks connected by color bonds separating from the space-time sheet of super-canonical blackhole in the production process, corresponds to the total quark mass and is about 170 MeV for ordinary proton and 87 GeV for M89 proton. This kind of picture about blackhole formation expected to occur in LHC differs from the stringy picture since a fusion of the hadronic mini blackholes to a larger blackhole is in question.
An interesting question is whether the ultrahigh energy cosmic rays having energies larger than the GZK cut-off (see the previous posting) are baryons, which have lost their valence quarks in a collision with hadron and therefore have no interactions with the microwave background so that they are able to propagate through long distances.
2. Ordinary blackholes as super-canonical blackholes
In neutron stars the hadronic space-time sheets could form a gigantic super-canonical blackhole and ordinary blackholes would be naturally replaced with super-canonical blackholes in TGD framework (only a small part of blackhole interior metric is representable as an induced metric).
- Hawking-Bekenstein blackhole entropy would be replaced with its p-adic counterpart given by
Sp= (M/m(CP2))2× log(p),
where m(CP2) is CP2 mass, which is roughly 10-4 times Planck mass. M corresponds to the contribution of p-adic thermodynamics to the mass. This contribution is extremely small for gauge bosons but for fermions and super-canonical particles it gives the entire mass.
- If p-adic length scale hypothesis p≈2k holds true, one obtains
Sp= k log(2)×(M/m(CP2))2 ,
m(CP2)=hbar/R, R the "radius" of CP2, corresponds to the standard value of hbar0 for all values of hbar.
- Hawking Bekenstein area law gives in the case of Schwartschild blackhole
S= hbar×A/4G = hbar×πGM2.
For the p-adic variant of the law Planck mass is replaced with CP2 mass and klog(2)≈ log(p) appears as an additional factor. Area law is obtained in the case of elementary particles if k is prime and wormhole throats have M4 radius given by p-adic length scale Lk=k1/2RCP2, which is exponentially smaller than Lp.
For macroscopic super-canonical black-holes modified area law results if the radius of the large wormhole throat equals to Schwartschild radius. Schwartschild radius is indeed natural: I have shown that a simple deformation of the Schwartschild exterior metric to a metric representing rotating star transforms Schwartschild horizon to a light-like 3-surface at which the signature of the induced metric is transformed from Minkowskian to Euclidian (see this).
- The formula for the gravitational Planck constant appearing in the Bohr quantization of planetary orbits and characterizing the gravitational field body mediating gravitational interaction between masses M and m (see this) reads as
v0=2-11 is the preferred value of v0. One could argue that the value of gravitational Planck constant is such that the Compton length hbargr/M of the black-hole equals to its Schwartshild radius. This would give
hbargr/hbar0= GM2/v0 , v0=1/2 .
This is a natural generalization of the Nottale's formula to gravitational self interactions. The requirement that hbargr is a ratio of ruler-and-compass integers expressible as a product of distinct Fermat primes (only four of them are known) and power of 2 would quantize the mass spectrum of black hole. Even without this constraint M2 is integer valued using p-adic mass squared unit and if p-adic length scale hypothesis holds true this unit is in an excellent approximation power of two.
- The gravitational collapse of a star would correspond to a process in which the initial value of v0, say v0 =2-11, increases in a stepwise manner to some value v0≤1/2. For a supernova with solar mass with radius of 9 km the final value of v0 would be v0=1/6. The star could have an onion like structure with largest values of v0 at the core. Powers of two would be favored values of v0. If the formula holds true also for Sun one obtains v0= 3×17× 213 with 10 per cent error.
- Blackhole evaporation could be seen as means for the super-canonical blackhole to get rid of its electro-weak charges and fermion numbers (except right handed neutrino number) as the antiparticles of the emitted particles annihilate with the particles inside super-canonical blackhole. This kind of minimally interacting state is a natural final state of star. Ideal super-canonical blackhole would have only angular momentum and right handed neutrino number.
- In TGD light-like partonic 3-surfaces are the fundamental objects and space-time interior defines only the classical correlates of quantum physics. The space-time sheet containing the highly entangled cosmic string might be separated from environment by a wormhole contact with size of black-hole horizon. This looks the most plausible option but one can of course ask whether the large partonic 3-surface defining the horizon of the black-hole actually contains all super-canonical particles so that super-canonical black-hole would be single gigantic super-canonical parton. The interior of super-canonical blackhole would be space-like region of space-time, perhaps resulting as a large deformation of CP2 type vacuum extremal. Blackhole sized wormhole contact would define a gauge boson like variant of blackhole connecting two space-time sheets and getting its mass through Higgs mechanism. A good guess is that these states are extremely light.
For the revised p-adic mass calculations hadron masses see the chapters p-Adic mass calculations: hadron masses and p-Adic mass calculations: New Physics of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy". See also the chapter Quantum Astrophysics of "Classical Physics in Many-Sheeted Space-Time".