Planck Thermodynamics
Redefining Black Hole Endstates in Intent Tensor Theory
Abstract
In standard black hole thermodynamics, black holes possess finite temperature, entropy proportional to their event horizon area, and are predicted to evaporate via Hawking radiation. Intent Tensor Theory (ITT) presents a radical alternative: black holes evolve into stable, cold Planck Cores where entropy and temperature reach absolute limits.
This section formalizes a new thermodynamic regime based on recursive memory saturation, drift-lock dynamics, and bounded entropy production. The result: a calculable, thermodynamically cold, memory-locked object—still gravitational, but stable.
The Core Insight
When the Collapse Tension Substrate reaches maximum recursive depth, the system undergoes Planck-lock:
L -> 1 => sigma_theta = D(1 - L) -> 0Consequences of Planck-lock:
- Entropy production halts: sigma_theta = 0
- Temperature drops to zero: T_ITT = 0
- No further Hawking radiation
- Information preserved in memory-locked shell
This is the Planck Core—a cold, stable, non-singular gravitational object.
Black Hole vs. Planck Core
| Feature | GR/QFT Black Hole | ITT Planck Core |
|---|---|---|
| Collapse End State | Singularity (undefined curvature) | Planck Core (bounded recursion) |
| Horizon Definition | Event horizon (nonlocal) | Shell-lock threshold (recursive) |
| Temperature | T_H diverges as M decreases | T_ITT = 0 at Planck-lock |
| Entropy Scaling | S proportional to A/4 | S_max = n_max times Planck area times N_folds |
| Information Paradox | Present | Resolved (memory preserved) |
| Radiation | Thermal spectrum until evaporation | Emission halts at lock |
| Final State | Complete evaporation or remnant | Stable Planck Core |
Key Equations
The Master Equation: Entropy Production
sigma_theta = D(1 - L)Where D is drift magnitude and L is shell-lock.
ITT Temperature
T_ITT = T_0 * sigma_thetaTemperature is proportional to entropy production rate.
Planck-Lock Condition
L = 1 => sigma_theta = 0 => T_ITT = 0At perfect alignment, temperature vanishes.
Bounded Entropy
S_theta_max = n_max * ell_P^2 * N_fold_sitesEntropy has a recursion ceiling—it cannot grow without bound.
LOAD Identity Connection
gamma_ITT = sqrt(1 - A^2 * Tr(M)/Tr(M)_max)At maximum memory: gamma_ITT approaches 0 (time stops) and T_ITT approaches 0 (temperature vanishes).
Resolution of Paradoxes
The Information Paradox
GR Problem: Hawking radiation is thermal—information appears to be lost.
ITT Solution: Information is never destroyed. At Planck-lock, the memory tensor M_ij preserves all state information. No radiation carries information away. Unitarity is maintained.
The Firewall Paradox
GR Problem: Quantum mechanics requires an energetic firewall at the horizon.
ITT Solution: No firewall needed. The transition to Planck Core is smooth—a lock, not a barrier. Recursion halts before any paradox arises.
Observable Predictions
| Observable | GR Prediction | ITT Prediction |
|---|---|---|
| GW Ringdown | Exponential decay | Modified + echoes |
| Shadow Inner Edge | Soft gradient | Sharp cutoff |
| Hawking Final Burst | Expected | Absent |
| PBH Remnants | None | Stable cores |
| Late Thermal Signal | Increasing | Abrupt cutoff |
Philosophical Shift
General Relativity implies nature permits the breakdown of physics in singularities.
ITT insists on a computational ceiling: Reality cannot out-compute itself.
Gravity, entropy, and time all halt at full recursion depth. This marks a transition from geometry to information physics.
Where GR ends in mystery, ITT offers a boundary: the Planck Core. Rather than speculate on unphysical infinities, ITT delivers a calculable, thermodynamically cold, memory-locked object.
Documentation
- Planck Core Thermodynamics — Full thermodynamic formalism
- Observable Signatures — Predictions and experimental tests
- ITT vs. GR Comparison — Complete side-by-side analysis
- Foundational Physics — Recursive basis of thermodynamics
- Experiments and Falsifiability — How to test the theory
- Notation and Units — Complete symbol reference
GitHub Repository
Full source documentation: github.com/intent-tensor-theory/0.0_planck_thermodynamics
Quick Reference
| Quantity | Symbol | Key Equation |
|---|---|---|
| Entropy Production | sigma_theta | = D(1 – L) |
| Temperature | T_ITT | = T_0 * sigma_theta |
| Maximum Entropy | S_theta_max | = n_max * ell_P^2 * N_folds |
| Dilation Factor | gamma_ITT | = sqrt(1 – A^2 * mu) |
| Planck-Lock | — | L = 1 implies T = 0 |
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