Intent-Tensor-Theory

ITT vs. GR Comparison

Complete Side-by-Side Analysis: Black Holes in General Relativity vs. Planck Cores in Intent Tensor Theory

1. Fundamental Concepts

Concept General Relativity / QFT Intent Tensor Theory
Nature of Spacetime Continuous manifold Recursive substrate (CTS)
Gravity Source Mass-energy curves geometry Memory alignment creates curvature
Information Carrier Not specified / problematic Memory tensor M_ij
Time Coordinate / proper time Emergent from drift sigma_theta
Fundamental Scale Planck length ell_P Maximum recursion n_max

2. Black Hole Formation

Aspect GR/QFT ITT
Collapse Mechanism Gravitational contraction Recursive memory accumulation
Critical Threshold Schwarzschild radius r_s = 2GM/c^2 Shell-lock threshold L approaches 1
Horizon Type Event horizon (global) Recursive boundary (local)
Interior Spacetime continues inward Recursion depth increases
Endpoint Singularity Planck Core

3. Temperature

Property GR/QFT ITT
Formula T_H = hbar c^3 / (8 pi G M k_B) T_ITT proportional to sigma_theta
Mass Dependence T proportional to 1/M T approaches 0 as L approaches 1
Large Mass Cold Cold (agrees)
Small Mass Hot (diverges) Cold (approaches zero)
Zero Mass Limit T approaches infinity T = 0
Minimum Temperature None 0 K (at Planck-lock)
Maximum Temperature Unbounded Finite (bounded by D_max)

4. Entropy

Property GR/QFT ITT
Formula S = k_B c^3 A / (4 G hbar) S_max = n_max * ell_P^2 * N_folds
Basis Geometric (area) Computational (recursion)
Scaling S proportional to M^2 S proportional to n_max
Upper Bound Bekenstein bound Recursion ceiling
Information Encoding Surface holography Volume + shell memory
At Evaporation Decreases Saturates

5. Radiation

Property GR/QFT ITT
Mechanism Hawking radiation (pair creation) Drift-induced emission
Spectrum Thermal (blackbody) Modified thermal
Duration Until complete evaporation Until Planck-lock
Final State Complete evaporation Radiation ceases
Energy Output ~ M c^2 total Limited by sigma_theta
Final Burst Yes (gamma-ray) No

6. Endstate

Property GR/QFT ITT
Name Singularity / Remnant Planck Core
Curvature Infinite Bounded
Size Zero (point) r_PC ~ sqrt(n_max) * ell_P
Mass Zero or undefined Finite Planck Core mass
Temperature Undefined or infinity 0 K
Entropy Unclear S_theta_max
Stability Unstable (evaporates) Absolutely stable

7. Information

Property GR/QFT ITT
Information Paradox Present Resolved
Information Location Lost to singularity? Preserved in M_ij
Unitarity Violated or unknown Preserved
Retrieval Impossible after evaporation Never lost
Encoding Holographic (surface) Memory tensor (volume + shell)

8. Time Behavior

Property GR/QFT ITT
At Horizon Infinite redshift gamma_ITT decreases
At Singularity Undefined Time stops (gamma = 0)
Time Dilation Source Spacetime curvature Substrate load (LOAD identity)
Infalling Observer Reaches singularity in finite proper time Experiences lock
External Observer Never sees crossing Sees gradual lock

9. Quantum Effects

Property GR/QFT ITT
Hawking Radiation Thermal pair creation Drift-limited emission
Entanglement Firewall paradox Lock preserves entanglement
Quantum State Mixed after evaporation Pure (unitary evolution)
Planck-Scale Physics Unknown/singular Bounded recursion

10. Observational Predictions

Observable GR/QFT ITT
GW Ringdown Exponential decay Modified + echoes
Shadow Inner Edge Soft Sharp
Hawking Burst Expected Absent
PBH Remnants None Stable cores
Late Thermal Signal Increasing Cutoff

11. Summary Table

Feature GR/QFT Black Hole ITT Planck Core
End State Singularity Bounded Core
Temperature Diverges Zero
Entropy Area-scaled Recursion-bounded
Radiation Until evaporation Halts at lock
Information Lost? Preserved
Time Undefined at singularity Stops at lock
Stability Evaporates Absolutely stable
Paradoxes Information, Firewall Resolved

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