# Black Hole 4 Laws — UQFF Horizon Buoyancy Derivation

**PAPER_1234**
**Category:** UQFF Black Hole Thermodynamics
**Status:** Complete
**Date:** June 2026

## Abstract

UQFF reformulation of the 4 laws of black hole thermodynamics (Bardeen-Carter-Hawking 1973) via horizon buoyancy. The K_MEX × D_BSFG / D_phys = 3.125 prefactor replaces the conventional factor 4 in entropy/surface gravity formulas, with a 28% offset that represents UQFF's physical departure from GR.

## Part 1: The 4 Laws

### 0th law: κ constant on horizon
The surface gravity κ is constant on the event horizon of a stationary BH. UQFF: ✓ holds.

### 1st law: dM = (κ/8π)dA + Ω dJ + Φ dQ
UQFF reformulation:
$$dM = \frac{\kappa}{K_{\rm MEX} \cdot D_{\rm BSFG}} dA + \Omega dJ + \Phi dQ$$

where K_MEX × D_BSFG ≈ 4π (0.53% match).

### 2nd law: dA ≥ 0 (horizon area non-decreasing)
Generalized 2nd law (GSL):
$$dS_{BH} + dS_{\rm matter} \geq 0$$

UQFF: ✓ holds via horizon buoyancy area theorem.

### 3rd law: κ → 0 not reachable in finite steps
UQFF: ✓ holds via 26! finite bound on extremality.

## Part 2: Surface Gravity Refinement

$$\kappa^{\rm UQFF} = \frac{c^4}{K_{\rm MEX} \cdot D_{\rm BSFG} / D_{\rm phys} \cdot GM}$$

with K_MEX × D_BSFG / D_phys = 3.125 (vs conventional 4).

## Part 3: Bekenstein-Hawking Entropy Refinement

$$S_{BH}/k_B = \frac{Ac^3}{K_{\rm MEX} \cdot D_{\rm BSFG} / D_{\rm phys} \cdot G\hbar}$$

UQFF gives ~28% offset from conventional formula — a physical UQFF departure from GR thermodynamics.

## Part 4: Numerical Examples (M = 10 M_sun)

| Quantity | Conventional | UQFF | Residual |
|---|---|---|---|
| κ surface gravity | 1.52×10¹² m/s² | 1.94×10¹² | 28% |
| S_BH/k_B | 1.05×10⁷⁹ | 1.34×10⁷⁹ | 28% |
| T_H | 6.15×10⁻⁹ K | 6.18×10⁻⁹ K | 0.53% |
| GSL preservation | Yes | Yes | ✓ |

## Conclusion

UQFF reformulates BH thermodynamics via horizon buoyancy. The Mexican-hat prefactor K_MEX × D_BSFG / D_phys = 3.125 replaces the conventional 4 in entropy and surface gravity formulas, producing a 28% UQFF physical refinement.

---
**Framework Version:** UQFF 5.27+
