Black Hole Evolution

Once you accept that a black hole can be compressed by its surroundings, the rest is automatic. A compressed horizon cannot grow freely. Every physical quantity inside the geometry is forced to evolve in discrete ln 2 steps. This is not a modelling choice. It is the only way the equations remain self–consistent when entropy and information approach equality.

For a black hole undergoing s discrete ln 2 compression steps, the scaling ladder is:

Mass = M₍s₎ = M₍earlier₎ / (ln 2)^(+1s)

Density = ρ(s) = ρ_earlier / (ln 2)^(+1s)

Radius = R(s) = R_earlier / (ln 2)^(+1s)

Entropy (Nats) = S(s) = S_earlier / (ln 2)^(+3s)

Information (Bits) = Nbits(s) = N_earlier / (ln 2)^(+2s)

Curvature = k(s) = k_earlier / (ln 2)^(−1s)

Rotation = ω(s) = ω_earlier / (ln 2)^(+2s)

Local Cosmic Time = t(s) = t_earlier / (ln 2)^(+1s)

Every quantity moves in lockstep. One ln 2 step produces the transformation:

M / (ln 2)^1 = R / (ln 2)^1 = t / (ln 2)^1 = S / (ln 2)^3 = N / (ln 2)^2 = k / (ln 2)^(−1) = ω / (ln 2)^2 = ρ / (ln 2)^1

This is the geometric fingerprint of black hole compression. Every physical quantity scales in powers of ln 2. Nothing escapes it.

Relaxed → Standard → Compressed EXAMPLE

To make the ladder explicit, consider three states of the same black hole:

• r: relaxed
• s: standardised
• c: compressed

The numerical values are irrelevant; the pattern is not.

Nr = 1.67676845344 × 10^85 → Ns = 2.41906553251 × 10^85 → Nc = 3.48997384733 × 10^85 → 5.03496796238 × 10^85

Rr = 3.10873872313 × 10^7 → Rs = 3.73397574342 × 10^7 → Rc = 4.48496193928 × 10^7 → 5.38698828783 × 10^7

Sr = 0.96763437052 × 10^85 → Ss = 1.67676845344 × 10^85 → Sc = 2.90559381940 × 10^85 → 5.03496796238 × 10^85

Mr = 2.09309967094 × 10^34 → Ms = 2.51406891859 × 10^34 → Mc = 3.01970451535 × 10^34 → 3.62703476130 × 10^34

ρr = 0.95981343132 × 10^11 → ρs = 1.15285342062 × 10^11 → ρc = 1.38471807755 × 10^11 → 1.66321591280 × 10^11

At this point, one fact becomes impossible to ignore - Everything scales in powers of ln 2. Even the universe

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Universe Evolution

For the universe undergoing s discrete ln 2 decompression steps, the ln 2 ladder is:

Mass = M (s) = M_earlier

Density = ρ(s) = ρ_earlier / (ln 2)^(-3s)

Radius = R(s) = R_earlier / (ln 2)^(+1s)

Entropy (Nats) = S(s) = S_earlier / (ln 2)^(+2s)

Information (Bits) = Nbits(s) = N_earlier / (ln 2)^(+3s)

Curvature = k(s) = k_earlier / (ln 2)^(−1s)

Rotation = ω(s) = ω_earlier / (ln 2)^(-2s)

Local Cosmic Time = t(s) = t_earlier / (ln 2)^(+1s)

Every quantity moves in lockstep. One ln 2 step produces the transformation:

M = R / (ln 2)^1 = t / (ln 2)^1 = S / (ln 2)^2 = N / (ln 2)^3 = k / (ln 2)^(−1) = ω / (ln 2)^(-2) = ρ / (ln 2)^(-3)

Universe Evolution Example

From birth to now, the universe has expanded through 

from Planck to end of tunnelling, s(planck) = 240.8991694

from end of tunnelling to now, s(tunnel) = 144.615410274

from Planck to now, s(total) = 385.5145797

discrete ln 2 steps.

The value of s in the example below is estimated, as are the values below.

What is important is the ln2 relationship the example demonstrates.

From Planck to Now, using realistic values based on this framework:

Cosmic Time_now = 1.24674E+18 s = 39.5 Gyr = 5.391E-44 / (ln 2)^(1s)

Local Time_now = 4.59507E+17 s = 14.56 Gyr = 1.98695E-44 s / (ln 2)^(1s)

Radius_now = 3.738E+26 m = 1.616E-35 / (ln 2)^(1s)

Volume_now = 2.18713E+80 m^3 = 1.7683E-104 / (ln 2)^(3s)

Curvature_now = 2.6755E-27 m−1 = 6.18743E+34 / (ln 2)^(−1s)

Rotation rate_now = 6.43355E-37 rad/s = 3.44082E+86 / (ln 2)^(−2s)

Density_now = 5.66038E-26 kg m−3 = 1.23075E+96 / (ln 2)^(−3s)

Entropy_now = 1.1385E+177 = 3.74234E-09 / (ln 2)^(2s)

Information_now = 2.633E+238 = 3.74234E-09 / (ln 2)^(3s)

Hubble Rate_Now = 9.8542E-20 = 2.2789E+42 / (ln 2)^(-1s)

Cosmological Constant_Now = 3.24132E-55 = 1.73354E+68 / (ln 2)^(-2s)

Mass at birth if tunnelled in = M_Planck = 2.17634E-08 at T = 5.391E-44 s

Mass at end of Tunnelling = M_Tunnel = 1.2380E+55 at T = 1.1931E-05 s (specific time not important)

Mass from M_Tunnel = constant = 1.238E55 kg.

The choice of how mass enters the universe, if at all, is irrelevant to the equations and numbers overall. 

Only early universe development is affected