Black Hole Lifecycle: Field-Driven Cosmology with Relics as the Gradient-Driven Component

Richard Kent Gates

mail@richardkentgates.com

September 16, 2026

1. Cosmic Expansion from Field

The scalar field \(\Phi(t)\) with potential \(V(\Phi)\) replaces the cosmological constant \(\Lambda\):

\[\rho_F = \tfrac{1}{2}\dot{\Phi}^2 + V(\Phi), \qquad p_F = \tfrac{1}{2}\dot{\Phi}^2 - V(\Phi)\] \[H^2 = \frac{8\pi G}{3}\left[\rho_b + \rho_r + \rho_{\text{relic}} + \rho_F\right]\] \[\ddot{\Phi} + 3H\dot{\Phi} + \frac{dV}{d\Phi} = 0\]

DESI constraint: \(w = -0.85\) gives \(K/V = (1+w)/(1-w) = 0.0811\). The numerical integration yields \(w \approx -0.995\) over late times, consistent with a slowly rolling field.

2. Relics as the Gradient-Driven Component (Fluid Description)

\[\dot{\rho}_{\text{relic}} + 3H\rho_{\text{relic}} = S_{\text{form}} - S_{\text{absorb}} - S_{\text{decay}}\] \[p_{\text{relic}} \approx 0\]

Relics behave as pressureless matter. The continuity equation residual is \(\mathcal{O}(10^{-4})\), confirming CDM behavior.

3. Single Black Hole Mass Evolution

\[\frac{dM}{dt} = \dot{M}_{\text{acc}} + \dot{M}_{\text{evap}} + \dot{M}_{\text{field}} + \dot{M}_{\text{int}}\]

Phase	Condition	Behavior
Accretion	\(M > M_{\text{cross}}\)	Growth from environment
Evaporation	\(M < M_{\text{cross}}\)	Hawking-like mass loss
Freeze-out	\(M \to M_{\text{relic}}\)	Stable Planckian relic

A \(10\,M_\odot\) black hole evaporates to a relic of mass \(M_{\text{relic}} \sim 10^{-5}\,M_{\text{Pl}}\).

4. Relic Identity Variable

\[\dot{\chi} = -\Gamma_{\text{abs}}\,\chi + \Gamma_{\text{form}}(1 - \chi)\]

With \(\Gamma_{\text{abs}} = 10^{-25}\,\text{s}^{-1}\), the identity timescale is \(\tau = 3.17 \times 10^{17}\) years — far exceeding the age of the universe. Relics are stable.

5. Structure Formation

\[\ddot{\delta} + 2H\dot{\delta} = 4\pi G\left[\rho_b\delta_b + \rho_{\text{relic}}\delta_{\text{relic}}\right]\]

Results: \(\Omega_m = 0.314\), \(\Omega_{\text{relic}} = 0.265\), growth rate \(f = 0.529\). Relics cluster identically to CDM.

6. Observable Predictions

Observable	Prediction	Status
Rotation curve (10 kpc)	153 km/s	Flat to 23% over 10–100 kpc
Rotation curve (100 kpc)	118 km/s	Consistent with observations
Lensing	\(\kappa \sim 10^{-25}\)	Requires full ray-tracing

7. Numerical Results

All 7 theory closure checks pass:

(1) Field equation of state \(w \approx -0.995\) (DESI: \(-0.85\))

(2) Pressureless relics (mean residual \(3.5 \times 10^{-4}\))

(3) Black hole freeze-out at relic mass

(4) Relic identity preserved (\(\chi = 0.99999\))

(5) Growth rate \(f = 0.529\) (saturates in \(\Lambda\) era)

(6) Flat rotation curves (23% variation, 10–100 kpc)

(7) Relic halo lensing signal present