Unified Recursive Organizational Theory: A Universal Framework from Biological to Cosmic Holography

Physics has developed dedicated theories of entropy, holography and information conservation only for black holes, because only a black hole compresses information to the capacity limit of its surface and forces the question of where the information that enters it goes; if black holes give birth to new universes, that information can only be passed on to the next generation, which corresponds to the concentration of information storage and transmission in the cell nucleus and the germ cells of living organisms. On this basis we map biological holography to cosmic scales. The extension rests on three previous papers and is kept consistent with their quantitative results: the domain–boundary organizing principle and biological holography are taken from the first; the 2dm axiom, the dark-energy capsule Ec and the cosmological residual potential from the second; and the relational decomposition of black-hole entropy, two-level quantization, last-in-first-out, the distribution of entropy over the two horizons of a Kerr black hole and the existence criterion from the third; their derivations are not repeated. On this basis we obtain the following results. (1) There is a single formation criterion for black holes: the density of a region reaches the mean black-hole density ρc/N2 corresponding to the number N of capsules it contains (ρc ≈ 1.54 × 1095 kg/m3). The combination of two Ec is the special case N = 2; a “density clock” expressed in the local density gives N = t/tP without recourse to the Hubble horizon; at the TOV limit, the mean density required for neutron-star collapse is comparable to the central density of a neutron star. (2) The fate of early black holes is set by the “critical mass” Mcrit(t) at which the background temperature equals the Hawking temperature, which plays the role of the critical nucleus in crystallization from solution: the earliest N = 2 seeds evaporate within about 10−40 s, and only black holes of mass ≳ 5 × 1011 kg, i.e. formed where the local density is below about 2.9 × 1056 kg/m3, survive to the present. (3) Low-mass primordial black holes cannot dominate star formation and can only be engulfed passively; in the present framework, Population III stars may commonly contain black-hole cores, while present-day ordinary stars are very unlikely to contain one. (4) The horizon structure of a black hole corresponds to a cell: the event horizon corresponds to the outer nuclear membrane and the Cauchy horizon to the inner nuclear membrane; the inner interface Ri = Rs/2 given by force balance depends only on the total energy and is the boundary that confines the capsule packs, and in the Schwarzschild case, which has no inner horizon, it is the counterpart of the inner nuclear membrane. The sum of the two horizon areas is always four times the area of the inner interface; at spin χ = √3/2 the inner horizon crosses Ri, a division that coincides with Smarr’s critical value for embedding the outer horizon and separates black holes into prokaryotic and eukaryotic types; a cosmic egg cell must be eukaryotic. The nucleus contains the Ec packs registered in packing order, their self terms and their pairwise relations. (5) Our universe arose from the burst of a parent black hole: at the burst the outer horizon of the parent black hole converts directly into the Hubble sphere of the parent universe, after which the Hubble sphere grows with the universe and always lies at its own Schwarzschild radius; outside black holes lies the Ec background shared by all generations; the remnant of the parent black hole still exists. The burst criterion follows from the existence criterion for black holes: the difference of the areal radii of the two horizons is not smaller than 2ℓp, and the last accretion that brings in angular momentum takes the separation below this lower limit, so that the registrations on the two horizons mix and can no longer be distinguished, and the structure breaks and bursts. A black-hole burst differs from pack-by-pack evaporation: it is a release of all capsule packs as a whole, the bulk of the matter converting together with the horizon, the throat jet being only a local channel; the relations as a whole become the organizational code of the new universe and recombine according to the code, so the burst is not constrained by the tunnelling probability and does not violate information conservation. (6) Ec has only three evolutionary pathways: remaining free, i.e. the background shared by all generations (dark energy); re-clustering into black holes where the density reaches ρc/N2 (dark matter); and being unpacked into radiation that condenses into particles and atoms (visible matter). What the burst distributes is only matter: the dark-matter part clusters preferentially at the highest density and the rest dilutes uniformly with the expansion; the ratio of dark to visible matter is set mainly at the burst. (7) The implicate and explicate orders are the internal and external readings of the same set of relations. We also discuss the isomorphism of transgenerational pre-setting in germ cells and in cosmic evolution, and the observational clues that the CMB “axis of evil”, the Cold Spot and supermassive black holes may form an ancestral–parent–child “three generations in one frame”.