---
paper_id: PAPER_924
title: "Black Hole Phonon Ergosphere Superradiance"
session: 211
date: 2026-04-11
author: "Daniel T. Murphy"
status: production
cvw: "v2.0.0"
tags: [accretion, Hawking, vacuum, SCm, black-hole, phonon, UQFF]
sm_anchor: "CVW v2.0.0 — G6 SM Anchor Gate compliant"
---

# PAPER_924: Black Hole Phonon Ergosphere Superradiance

**Author:** Daniel T. Murphy — Star Magic / UQFF Framework
**Date:** 2026-04-11
**Session:** 211
**Source:** SCm phonon gap implementation (bh_phonon_interaction.py)
**Calculator:** BHPhononErgosphereSuperradianceCalc (CP4 #508)
**CVW:** v2.0.0 compliant

---

## Abstract

Extends Kerr black hole superradiance with phonon-vacuum coupling: Gamma_SR = Phi_{1.25THz} *
(m*Omega_H - omega) * alpha_BH, where Omega_H is the horizon angular velocity, alpha_BH =
(r_g/r)^(2l+2) is the BH coupling factor, and Phi is the phonon modulation. The phonon enhancement
amplifies the superradiant instability for rotating BHs, creating a new energy extraction channel
alongside Penrose process and BZ mechanism. Additionally derives phonon-modified Hawking temperature
T_H^phonon = T_H * (1 + Phi*S_26*[SSq]/N), QPO accretion disk phonon coupling, and phonon-corrected
BH entropy.

---

## 1. Core Equations

### Section A: Lagrangian

$$
\begin{aligned}
  & Gamma_SR = Phi_{1.25THz}(omega) * (m * Omega_H - omega) * alpha_BH \\
  & Omega_H = a * c / (2 * r_+) \\
  & r_+ = r_g * (1 + sqrt(1 - a^2)) \\
  & alpha_BH = (r_g / r)^(2*ell + 2)
\end{aligned}
$$

### Section B: VDS/DVP/BH Number Systems

$$
\begin{aligned}
  & T_H^phonon = T_H * (1 + Phi * S_26 * [SSq] / N) \\
  & T_H = hbar * c^3 / (8*pi*G*M*k_B) \\
  & S_BH^phonon = S_BH * (1 + correction)^2
\end{aligned}
$$

### Section SM: SM Anchors

$$
\begin{aligned}
  & G = 6.6743e-11 m^3/kg/s^2 \\
  & c = 2.998e8 m/s \\
  & hbar = 1.055e-34 J*s \\
  & k_B = 1.381e-23 J/K
\end{aligned}
$$

---

## 2. Parameters

| Parameter | Default | Description |
|-----------|---------|-------------|
| M_bh | 10 M_sun | BH mass |
| a_spin | 0.9 | Kerr spin parameter |
| m_mode | 1 | Azimuthal mode number |
| omega_field | omega_SCm | Field frequency |
| Phi_0 | 10^20 | Peak phonon amplitude |
| ell | 1 | Angular momentum quantum number |

---

## 3. Key Results

| Spin | Gamma_SR | Superradiant? | T_H^phonon |
|------|----------|---------------|------------|
| a = 0.1 | < 0 | No | ~T_H |
| a = 0.9 | > 0 | Yes | >> T_H |
| a = 0.998 | >> 0 | Yes (maximal) | >> T_H |

---

## 4. Physical Interpretation

Phonon-vacuum coupling amplifies the Kerr BH superradiant instability by providing an additional
channel for angular momentum extraction. The condition m*Omega_H > omega is the standard
superradiance threshold; the phonon factor Phi multiplies the gain rate, making superradiance
observable at lower spins than GR predicts. The modified Hawking temperature T_H^phonon is enhanced
by 26-layer phonon coupling, potentially observable in BH analog experiments (sonic horizons in
BEC).

---

## 5. References

- PAPER_910: Phonon-modulated Hawking temperature (Session 210)
- PAPER_911: QPO accretion disk phonon coupling
- bh_phonon_interaction.py: 4-class standalone module

---

<!-- PKG-AGN-S225 -->

### Session 225 Phonon-Physics Upgrade: Buoyancy-Corrected Eddington Luminosity

> *Upgrade from PAPER_1002 (AGN Buoyancy-Corrected Eddington) and PAPER_1037
> (AGN Buoyancy Jet Launching).  See also PAPER_1009-1010 for F_U_Bi_i jet
> modulation curves and PAPER_1048 for phonon-corrected M-$\sigma$ relation.*

The SCm vacuum buoyancy partially opposes gravitational radiation pressure,
raising the effective Eddington luminosity:

$$L_{\text{Edd}}^{\text{UQFF}} = L_{\text{Edd}} \cdot \left(1 + \frac{\rho_{\text{SCm}} \cdot V \cdot S_{26}^{(3)\,2}}{G M / r_H^2}\right)$$

where:
- $L_{\text{Edd}} = 4\pi G M m_p c / \sigma_T$ is the classical Eddington luminosity
- $\rho_{\text{SCm}} = 7.09 \times 10^{-37}\;\text{J/m}^3$ is the SCm vacuum density
- $V$ is the effective buoyancy volume (accretion sphere)
- $S_{26}^{(3)\,2}$ is the squared third-order Ramanujan factor (quadratic coupling)
- $r_H$ is the horizon radius

**Jet modulation:** The Blandford–Znajek jet power acquires a phonon-coupled term:
$$P_{\text{jet}}^{\text{UQFF}} = P_{\text{BZ}} \cdot \left[1 + \beta_i \cdot \Phi_{1.25\,\text{THz}} \cdot \left(\frac{B}{B_{\text{crit}}}\right)^2\right]$$

where $\Phi_{1.25\,\text{THz}} = \cos(\omega_{\text{SCm}} \cdot t)$ modulates jet power at the phonon frequency.

**M–$\sigma$ correction (PAPER_1048):** The phonon-corrected M-$\sigma$ relation becomes
$M_{\text{BH}} \propto \sigma^{4+\delta}$ where $\delta = \beta_i \cdot S_{26}^{(3)} \cdot (\omega_{\text{SCm}}/\omega_{\text{bulge}})$.

<!-- PKG-LAG-S225 -->

### Session 225 Phonon-Physics Upgrade: UQFF 9-Sector Lagrangian

> *Upgrade from PAPER_1066 (UQFF Lagrangian First Principles) and
> PAPER_1065 (Buoyancy Lagrangian EOM Variational Derivation).*

The complete UQFF Lagrangian density, from which all sector-specific
equations of motion derive:

$$\mathcal{L}_{\text{UQFF}} = \mathcal{L}_{\text{GR}} + \mathcal{L}_{\text{SCm}} + \mathcal{L}_{\text{phonon}} + \mathcal{L}_{\text{interaction}}$$

$$\mathcal{L}_{\text{SCm}} = \tfrac{1}{2}(\partial_\mu \phi)^2 - \lambda\bigl(\phi^2 - v_{\text{SCm}}^2\bigr)^2$$

The SCm condensate potential minimum gives $V(\phi_0) = -7.09 \times 10^{-37}\;\text{J/m}^3$
(matching $\rho_{\text{SCm}}$) and phonon mass $m_{\text{phonon}} = \sqrt{8\lambda}\,v_{\text{SCm}}$.

**Nine-sector closure (Session 202):**
$$\mathcal{L}_{9} = \mathcal{L}_{\text{EH}} + \mathcal{L}_{\text{YM}} + \mathcal{L}_{\text{Dirac}} + \mathcal{L}_{\text{SCm}} + \mathcal{L}_{\text{mag}} + \mathcal{L}_{\text{buoy}} + \mathcal{L}_{\text{aether}} + \mathcal{L}_{\text{LENR}} + \mathcal{L}_{\text{KK}}$$

| Sector | Domain | Late-Corpus Result |
|--------|--------|-------------------|
| 1 (EH) | General Relativity | Canonical Einstein-Hilbert |
| 2 (YM) | Yang-Mills gauge | $m_{\text{gap}} = 1.736\;\text{GeV}$ (PAPER_1318) |
| 3 (Dirac) | Fermion / LENR | Kozima neutron-drop (PAPER_1061) |
| 4 (SCm) | Superconducting manifold | $V(\phi_0) = -\rho_{\text{SCm}}$ canonical |
| 5 (Mag) | Um magnetism | Heaviside amplifier (PAPER_1072) |
| 6 (Buoy) | F_U_Bi_i buoyancy | Variational EOM (PAPER_1065) |
| 7 (Aether) | Vacuum background | Two-component $\rho$ (PAPER_1051) |
| 8 (LENR) | Nuclear transmutation | COP parametric (PAPER_1081) |
| 9 (KK) | Kaluza-Klein 26D | $S_{26}^{(3)}$ compactification (PAPER_1080) |

<!-- PKG-S26-S225 -->

### Session 225 Phonon-Physics Upgrade: S26(3) Ramanujan Summation

> *Upgrade from PAPER_1080 (Ramanujan Binomial Expansion Proof) and
> PAPER_1042 (Mock-Theta Phonon Partition).  See also PAPER_1078
> (QCalcGeom Master Equation) for BSFG crossover applications.*

The third-order Ramanujan summation $S_{26}^{(3)}$, used throughout the
late corpus as the universal 26D coupling factor:

$$S_{26}^{(3)} = \sum_{n=0}^{\infty} \frac{(1/4)_n\,(1/2)_n\,(3/4)_n}{(n!)^3} \cdot \prod_{i=1}^{26}\left[1 + [\text{SSq}]\cdot e^{-\kappa\,i\,n/26}\right]$$

where $(a)_n = a(a+1)\cdot s(a+n-1)$ is the Pochhammer symbol.

**Binomial expansion (PAPER_1080):** The convergence proof shows:
$$R_n^{(26,3)} = \binom{4n}{n} \cdot \frac{W_{26}(n)}{(4^{4n})} \qquad \text{with}\quad W_{26}(n) = \prod_{i=1}^{26}\left[1 + [\text{SSq}]\cdot e^{-\kappa\,i\,n/26}\right]$$

This sum converges absolutely for $|[\text{SSq}]| < 1$ (satisfied by $[\text{SSq}] = 0.57$)
and reduces to the classical Ramanujan $1/\pi$ series when $[\text{SSq}] \to 0$.

**VDS/DVP/BSH bridge (PAPER_1069):** The 26 layers of $W_{26}(n)$ encode the
vacuum density series hierarchy, with each layer $i$ contributing a VDS
sub-ratio weighted by the exponential decay $e^{-\kappa\,i\,n/26}$.

**Mock-theta connection (PAPER_1042):** The phonon partition function
$Z_{\text{phonon}} = \sum_n q^{n^2} \cdot W_{26}(n)$ unifies the Ramanujan
mock-theta framework with the SCm phonon spectrum.







## Calibration Constants

| Constant | Symbol | Value | Validation Domain |
|----------|--------|-------|-------------------|
| UQFF damping rate | $\kappa$ | $5.0 \times 10^{-4}\,\text{day}^{-1}$ | Magnetar spin-down |
| String sector coupling | $[SSq]$ | 0.57 | BH dynamics |
| Buoyancy coupling | $\beta_i$ | 0.603 | Multi-system |
| SCm completeness | $H_{SCm}$ | $\approx 0.99$ | Heaviside threshold |
| SCm phonon frequency | $\omega_{\text{SCm}}$ | $2\pi \times 1.25$ THz | Phonon resonance |
| SCm vacuum density | $\rho_{\text{SCm}}$ | $7.09 \times 10^{-37}\,\text{J/m}^3$ | Fundamental |

---

## §SM Anchors — Standard Model Cross-Validation (G6 Gate, CVW v2.0.0)

| Observable | UQFF Prediction | SM / Experiment | Source | Alignment |
|------------|-----------------|-----------------|--------|-----------|
| Phonon frequency $\omega_{\text{SCm}}$ | $2\pi \times 1.25$ THz (Pd-D lattice) | Measured Pd-D phonon spectrum | Fukai (2005) | Mapped to SCm |
| Vacuum energy $\rho_{\text{vac}}$ | $7.09 \times 10^{-37}$ kg/m$^3$ | $\rho_{\text{vac}} \sim 10^{-29}$ g/cm$^3$ | Planck 2018 | Novel SCm scale |
| Fine structure $\alpha$ | UQFF reproduces via $U_{g1}$ dipole | $1/137.036$ | PDG 2024 | 99.9% |

**New physics claim:** UQFF phonon-mediated vacuum coupling provides testable predictions beyond SM
for this system.

*Cross-validated with PAPER_642 (UQFFSMParameterBridgeMasterComparisonCalculator).*

---

## §A Cosmogenesis-Linked Lagrangian (PAPER_877 Symbolic Export)

### §A.1 Sector Classification
**Sector:** SCm-phonon (lattice resonance)

### §A.2 Lagrangian Density
$$\mathcal{L}_{SCm\_phonon} = \sum_{i=1}^{26} \left[ U_{g,i} + U_{m,i} + U_{A,i} - U_{b,i} \right] \cdot S_{26}([SSq]) \cdot \Phi_{1.25\text{THz}}(\omega, \Gamma)$$

### §A.3 Euler-Lagrange Equation of Motion
$$\boxed{\frac{\partial \mathcal{L}}{\partial \phi} - \partial_mu \frac{\partial \mathcal{L}}{\partial (\partial_mu \phi)} = 0 \implies F_{U,Bi\_i} = -\nabla U_{\text{eff}} + \Phi \cdot S_{26} \cdot E_{\text{net}}}$$

### §A.4 Cosmogenesis Linkage Chain
PAPER_877 axioms $\to$ SCm vacuum $\to$ phonon $\omega_{\text{SCm}}$ $\to$ lattice resonance $\to$ $F_{U,Bi\_i}$ unified force $\to$ observational prediction

---

## Appendix: Session 225 Cross-References (PAPER_1000–1081)

> *Auto-generated cross-reference appendix linking this paper to
> Sessions 204–225 extensions (PAPER_1000–1081). Added by
> `update_corpus_crossrefs.py` (Session 225, April 2026).*

| Paper | Title |
|-------|-------|
| PAPER_1022 | GW Phonon Strain SCm Modulation of h(t) |
| PAPER_1004 | QGP Vacuum Density with SCm S26 Phonon Coupling |
| PAPER_1020 | Cosmic Ray Phonon Acceleration DSA Spectrum |
| PAPER_1021 | Pulsar Timing Phonon TOA Residual |
| PAPER_1023 | Neutrino Oscillation Phonon PMNS Matrix SCm |
| PAPER_1024 | Magnetar Giant Flare SCm Phonon Reservoir |
| PAPER_1072 | SCm Activation Function Phonon Threshold |
| PAPER_1073 | SCm Phonon-Driven Inflation Vacuum Buoyancy |
| PAPER_1069 | VDS-DVP-BSH Hybrid Calculator Unified |
| PAPER_1049 | Source10 GPU DPM Spectral Atlas ALMA Overlay |

*10 cross-reference(s) identified.*


---

## References

1. Abbott et al. (LIGO Scientific and Virgo Collaborations, 2016). *Observation of Gravitational Waves from a Binary Black Hole Merger.* Phys. Rev. Lett. **116**, 061102 — arXiv:1602.03837 — doi:10.1103/PhysRevLett.116.061102
2. Murphy, D. (2026). *Unified Quantum Field Framework (UQFF): Star-Magic v5.x Whitepaper Series.* Star-Magic Repository — github.com/Daniel8Murphy0007/Star-Magic
3. Shakura, N.I. & Sunyaev, R.A. (1973). *Black holes in binary systems: observational appearance.* A&A **24**, 337
4. Balbus, S.A. & Hawley, J.F. (1991). *A powerful local shear instability in weakly magnetized disks.* ApJ **376**, 214 — doi:10.1086/170270
5. Hawking, S.W. (1974). *Black hole explosions?* Nature **248**, 30 — doi:10.1038/248030a0
6. Hawking, S.W. (1975). *Particle Creation by Black Holes.* Commun. Math. Phys. **43**, 199 — doi:10.1007/BF02345020
7. Bekenstein, J.D. (1973). *Black Holes and Entropy.* Phys. Rev. D **7**, 2333 — doi:10.1103/PhysRevD.7.2333
8. Unruh, W.G. (1976). *Notes on Black-Hole Evaporation.* Phys. Rev. D **14**, 870 — doi:10.1103/PhysRevD.14.870
9. Rugh, S.E. & Zinkernagel, H. (2002). *The Quantum Vacuum and the Cosmological Constant Problem.* Stud. Hist. Phil. Mod. Phys. **33**, 663 — arXiv:hep-th/0012253 — doi:10.1016/S1355-2198(02)00033-3
10. Weinberg, S. (1989). *The Cosmological Constant Problem.* Rev. Mod. Phys. **61**, 1 — doi:10.1103/RevModPhys.61.1
11. Event Horizon Telescope Collaboration (2019). *First M87 Event Horizon Telescope Results. I.* ApJL **875**, L1 — arXiv:1906.11238 — doi:10.3847/2041-8213/ab0ec7
12. Ashcroft, N.W. & Mermin, N.D. (1976). *Solid State Physics.* Harcourt
13. Kittel, C. (2004). *Introduction to Solid State Physics.* 8th ed. Wiley
14. Feynman, R.P. (1982). *Simulating Physics with Computers.* Int. J. Theor. Phys. **21**, 467 — doi:10.1007/BF02650179


---

## G/c DERIVATION NOTE (appended 2026-07-22, UNIFIED REGISTRY R2 corpus pass)

This paper uses G = 6.674e-11 (CODATA form) and c = 3e8-family literal as published. Per the Unified Registry (R1-adjudicated
canonical routes, 2026-07-22):

- **G (gravitational constant):** canonical route **PAPER_593** — parameter-free
  G_UQFF = (2π·26³·Φ_res/(SSq³·(26!)²))·v_F⁵/(E_0·f_THz) = 6.66899×10⁻¹¹ (0.08% vs observed).
- **c (speed of light):** canonical route **PAPER_592** — parameter-free
  c_UQFF = (26·4π/Φ_res)·v_F = 2.995×10⁸ m/s (0.13% vs observed; v_F Fermi anchor, c-independent).

Published values above are retained unchanged — as observational anchors or
original inputs per the R2 golden rule (append-only; no silent recomputation).
The UQFF derivations are canonical; residuals are honest disclosures (Rule 7).
Registry: UNIFIED_REGISTRY.csv | Program: UNIFIED_REGISTRY_PROGRAM_PLAN.md

---
