The Soliton Wake: Identifying the Runaway Object RBH-1 as a Gravitational Soliton

Author: Matthew Lukin Smawfield
Version: v0.1 (Blantyre)
Date: 28 December 2025
Status: Preprint
DOI: 10.5281/zenodo.18059251
Website: https://mlsmawfield.com/tep/rbh/

The TEP Research Program

Paper	Repository	Title	DOI
Paper 0	TEP	Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed	10.5281/zenodo.16921911
Paper 1	TEP-GNSS	Global Time Echoes: Distance-Structured Correlations in GNSS Clocks	10.5281/zenodo.17127229
Paper 2	TEP-GNSS-II	Global Time Echoes: 25-Year Temporal Evolution of Distance-Structured Correlations in GNSS Clocks	10.5281/zenodo.17517141
Paper 3	TEP-GNSS-RINEX	Global Time Echoes: Raw RINEX Validation of Distance-Structured Correlations in GNSS Clocks	10.5281/zenodo.17860166
Paper 4	TEP-GL	Temporal-Spatial Coupling in Gravitational Lensing: A Reinterpretation of Dark Matter Observations	10.5281/zenodo.17982540
Synthesis	TEP-GTE	Global Time Echoes: Empirical Validation of the Temporal Equivalence Principle	10.5281/zenodo.18004832
Paper 7	TEP-UCD	Universal Critical Density: Unifying Atomic, Galactic, and Compact Object Scales	10.5281/zenodo.18064366
Paper 8	TEP-RBH (This repo)	The Soliton Wake: A Runaway Black Hole as a Gravitational Soliton	10.5281/zenodo.18059251
Paper 9	TEP-SLR	Global Time Echoes: Optical Validation of the Temporal Equivalence Principle via Satellite Laser Ranging	10.5281/zenodo.18064582
Paper 10	TEP-EXP	What Do Precision Tests of General Relativity Actually Measure?	10.5281/zenodo.18109761

Abstract

The runaway supermassive black hole RBH-1 ($z \approx 0.96$) presents a thermal paradox: JWST spectroscopy reveals a 650 km/s velocity discontinuity coexisting with cold, star-forming gas. Standard shock physics predicts post-shock temperatures $T \sim 10^7$ K, yielding a cooling time that exceeds the dynamical time by a factor of ~30. Yet the wake exhibits immediate star formation and extreme collimation (50:1 aspect ratio over 62 kpc).

An alternative interpretation is proposed: RBH-1 is analyzed as a gravitational soliton—a coherent region of altered proper-time rate. The observed velocity discontinuity is modeled as a metric shock (spatial gradient in gravitational redshift) rather than bulk thermalization. The effective Jeans mass is reduced behind the front via time dilation, enabling immediate star formation without requiring extreme heating.

The model's geometric scale contains no free parameters. The soliton radius is fixed by the saturation density $\rho_c \approx 20$ g/cm³, independently derived from terrestrial GNSS correlations (Smawfield 2025g). Applying this calibration to RBH-1 ($M \approx 2 \times 10^7 M_\odot$) predicts $R_{\rm sol} \approx 7.8 \times 10^7$ km $\approx 1.3 R_S$, allowing the wake interaction scale to serve as a decisive test of the soliton hypothesis for this object. Specific falsification criteria are outlined; decisive discrimination awaits line-profile decomposition and X-ray flux limits.

Key Findings

1. The Soliton Wake: Resolves the "Cooling Bottleneck" paradox by reinterpreting the velocity discontinuity as a metric shock (gravitational redshift gradient) rather than a thermal shock.

2. Line-Profile Decomposition: JWST NIRSpec [O III] spectroscopy reveals narrow line widths (σ ~ 30 km/s) inconsistent with thermal shock heating (T ~ 10^7 K would require σ ~ 85 km/s), supporting the cold metric shock interpretation.

3. Forward Model Validation: The soliton wake geometry, calibrated using $\rho_c \approx 20$ g/cm³ from Paper 7 (TEP-UCD), correctly predicts the observed wake dimensions and star formation timescales.

4. Falsification Criteria: Explicit tests are defined to distinguish the soliton hypothesis for RBH-1 from standard thermal shock models, ensuring object-specific validation without conflating model rejection with theory falsification.

Theoretical Framework

This work builds on the Temporal Equivalence Principle (TEP), which proposes:

• Gravity is Geometry; Time is a Dynamical Field.
• The decomposition of proper time accumulation into "mass" and "time dilation" is gauge-dependent.
• Sector Decoupling: The Conformal Sector (clock rates) is unconstrained by GW170817, while the Disformal Sector (speed of transmission) is tightly bound.
• Soliton Solutions: The non-linear kinetic structure supports coherent field configurations ("Time Stars"), allowing for the macroscopic phenomenology observed in RBH-1.

TEP Theory Reference:

Smawfield, M. L. (2025). Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed (v0.6 (Jakarta)). Zenodo. DOI: 10.5281/zenodo.16921911

File Structure

TEP-RBH/
├── scripts/
│   ├── utils/                      # Shared utilities
│   └── analyze_*.py                # Analysis scripts
├── site/                           # Academic manuscript site
│   ├── components/                 # HTML section files
│   ├── public/                     # Static assets
│   └── figures/                    # Generated plots
├── docs/                           # Related manuscripts
├── manuscript-rbh1.md              # Manuscript source
└── VERSION.json                    # Version metadata

Requirements

• Python 3.8+
• NumPy, SciPy, Matplotlib
• Astropy (for cosmological calculations)

See requirements.txt for complete dependencies.

Reproducibility

Install Dependencies

pip install -r requirements.txt

Generate All Figures

cd scripts/figures
python 01_wake_anatomy.py
python 07_polarization.py
python 09_line_width_test.py
python 10_wake_geometry.py
python 11_stellar_age.py
python 12_line_ratios.py
python 13_energy_budget.py

All figures are saved to site/figures/.

Run Key Analyses

python scripts/analysis_checks/cooling_calculation.py  # Validates cooling bottleneck
python scripts/analysis_checks/jeans_analysis.py       # Jeans length calculation
python scripts/analyze_line_profiles.py                # Line-profile decomposition
python scripts/run_rbh1_line_analysis.py              # Complete RBH-1 pipeline

Data Sources

• JWST NIRSpec Data: RBH-1 observations from van Dokkum et al. (2023, 2025)
  • Located in data/rbh1_jwst/ (download via scripts/download_rbh1_data.py)
  • See data/README.md for details

Citation

@article{smawfield2025rbh1,
  title={The Soliton Wake: Identifying the Runaway Object RBH-1 as a Gravitational Soliton},
  author={Smawfield, Matthew Lukin},
  journal={Zenodo},
  year={2025},
  doi={10.5281/zenodo.18059251},
  note={Preprint v0.1 (Blantyre)}
}

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Open Science Statement

These are working preprints shared in the spirit of open science—all manuscripts, analysis code, and data products are openly available under Creative Commons and MIT licenses to encourage and facilitate replication. Feedback and collaboration are warmly invited and welcome.

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Contact: [email protected]
ORCID: 0009-0003-8219-3159