### Blackhole production at LHC and replacement of ordinary blackholes with super-canonical blackholes

Tommaso Dorigo has an interesting posting about blackhole production at LHC. I have never taken this idea seriously but in a well-defined sense TGD predicts blackholes associated with super-canonical gravitons with strong gravitational constant defined by the hadronic string tension. The proposal is that super-canonical blackholes have been already seen in Hera, RHIC, and the strange cosmic ray events (see the previous posting). Ordinary blackholes are naturally replaced with super-canonical blackholes in TGD framework, which would mean a profound difference between TGD and string models.

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 α_{s}=α_{K}=1/4 is reduced. The condition that α_{K} has the same value for the super-canonical phase as it has for ordinary gauge boson space-time sheets gives hbar=26×hbar_{0}. 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 M_{107} hadron physics would have mass 934.2 MeV, very near to proton mass. The mass of their M_{89} 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 M_{89} 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
S

_{p}= (M/m(CP_{2}))^{2}× log(p),where m(CP

_{2}) is CP_{2}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≈2
^{k}holds true, one obtainsS

_{p}= k log(2)×(M/m(CP_{2}))^{2},m(CP

_{2})=hbar/R, R the "radius" of CP_{2}, corresponds to the standard value of hbar_{0}for all values of hbar. - Hawking Bekenstein area law gives in the case of Schwartschild blackhole
S= hbar×A/4G = hbar×πGM

^{2}.For the p-adic variant of the law Planck mass is replaced with CP

_{2}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 M^{4}radius given by p-adic length scale L_{k}=k^{1/2}R_{CP2}, which is exponentially smaller than L_{p}.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
hbar

_{gr}/hbar_{0}=GMm/v_{0}.v

_{0}=2^{-11}is the preferred value of v_{0}. One could argue that the value of gravitational Planck constant is such that the Compton length hbar_{gr}/M of the black-hole equals to its Schwartshild radius. This would givehbar

_{gr}/hbar_{0}= GM^{2}/v_{0}, v_{0}=1/2 .This is a natural generalization of the Nottale's formula to gravitational self interactions. The requirement that hbar

_{gr}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 M^{2}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 v
_{0}, say v_{0}=2^{-11}, increases in a stepwise manner to some value v_{0}≤1/2. For a supernova with solar mass with radius of 9 km the final value of v_{0}would be v_{0}=1/6. The star could have an onion like structure with largest values of v_{0}at the core. Powers of two would be favored values of v_{0}. If the formula holds true also for Sun one obtains v_{0}= 3×17× 2^{13}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 CP
_{2}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".

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