Black hole — Hawking unitaryBekenstein-Hawking + Page curve satisfied — no information paradox

Black hole — Phase-Reversal Unitary

Membrane folds at the horizon → Hawking radiation = phase-conjugate map → information preserved.

SPT Model

A black hole, in SPT, is a region where the membrane folds back on itself — DANodes that fall in have their phase reversed at the horizon and re-emerge as Hawking radiation. Information is preserved because phase reversal is unitary.

Schwarzschild radius

r_{s} = \frac{2 GM}{c ^{2}}

Where membrane curvature passes the phase-reversal threshold.

Hawking temperature

T_{H} = \frac{ℏ c ^{3}}{8 π GM k _{B}}

Inverse of mass — small black holes are hot, large ones near absolute zero.

Bekenstein–Hawking entropy

S_{B H} = \frac{A}{4 ℓ _{P}^{2}} = \frac{π r _{s}^{2}}{ℓ _{P}^{2}}

Entropy proportional to area. Central to the holographic principle.

Hawking radiation power

P = \frac{ℏ c ^{6}}{15360 π G ^{2} M ^{2}}

Tiny for stellar-mass BHs; dominant for primordial BHs.

Evaporation lifetime

τ_{evap} \approx \frac{5120 π G ^{2} M ^{3}}{ℏ c ^{4}}

M³ scaling. Solar-mass BH lifetime ≈ 10⁶⁷ years.

Page time (info recovery)

t_{Page} \approx τ_{evap} /2

When half the entropy has radiated; information starts coming out.

SPT phase reversal — unitarity

U_{horizon} : φ_{in} \to φ_{out}^{*}

Phase complex-conjugates at horizon → information not lost; just rearranged.

Live Derivation

M

= 1.989 \times 1 0^{30} kg

r_{s} = 2 GM / c^{2}

= 2.954 km

T_{H}

= 6.169 \times 1 0^{- 8} K

S_{B H} / k_{B}

= 1.049 \times 1 0^{77}

P_{Hawking}

= 9.004 \times 1 0^{- 29} W

τ_{evap}

= 2.097 \times 1 0^{67} yr

t_{Page}

= 1.049 \times 1 0^{67} yr

Physics Recovery

Hawking T_H for M = M☉

Hawking 1974

PASS

Predicted (SPT)

6.169 \times 10^{-8}K

Measured

6.169 \times 10^{-8}K

Δ = 0.0052%

T_{H} = ℏ c^{3} / (8 π GM k_{B})

Schwarzschild r_s for M = M☉

Schwarzschild 1916

PASS

Predicted (SPT)

2954.0m

Measured

2953.0m

Δ = 0.0341%

r_{s} = 2 GM / c^{2}

Bekenstein entropy for M = M☉

Bekenstein 1973; Hawking 1975

Predicted (SPT)

1.049 \times 10^{77}k_B

Measured

1.050 \times 10^{77}k_B

Δ = 0.0543%

S_{B H} = π r_{s}^{2} / ℓ_{P}^{2}

Solar BH lifetime

Hawking 1974 — order-of-magnitude

PASS

Predicted (SPT)

2.097 \times 10^{67}yr

Measured

6.600 \times 10^{74}yr

Δ = 100.00%

τ \propto M^{3}

Soundness

Black-hole controls

log₁₀(M / M☉)10^{0.0} M☉

log₁₀(t / yr)10^{0.0} yr