1 - Encoded Equilibrium in the Stellar Graveyard: Evidence from Compact Object Mass Distributions

 1 - Encoded Equilibrium in the Stellar Graveyard: Evidence from Compact Object Mass Distributions

DOI: To Be Assigned

John Swygert

March 7, 2026

Abstract

Recent observations from the global gravitational-wave detector network have dramatically expanded the catalog of compact object mergers. These detections reveal structured boundaries in the mass distribution of stellar remnants, including neutron stars and black holes. This paper examines observational data from the LIGO–Virgo–KAGRA collaborations and associated electromagnetic observations to evaluate whether these distributions reflect equilibrium conditions governing stellar collapse. The data suggest that stellar remnants populate well-defined regions constrained by fundamental physical limits, including neutron degeneracy pressure, gravitational instability, and pair-instability supernova processes. The resulting distribution resembles an equilibrium envelope in compact-object mass space.

1. Introduction

The detection of gravitational waves in 2015 opened a new observational window into the universe. The global detector network consisting of the LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Observatory has since observed dozens of compact binary mergers involving black holes and neutron stars. These observations provide the first statistically meaningful sample of compact object masses formed through stellar collapse. When visualized collectively, the distribution of these masses appears structured rather than random. This raises the question: do these distributions reflect equilibrium conditions imposed by fundamental physical limits?

2. Observational Data

The LIGO–Virgo–KAGRA (LVK) Gravitational-Wave Transient Catalog 4.0 (GWTC-4.0) documents 218 events from compact binary mergers. These include binary black hole (BBH), binary neutron star (BNS), and neutron star–black hole (NSBH) systems. Electromagnetic observations complement these detections, providing mass estimates for neutron stars through radio pulsar timing and x-ray binary measurements, and for black holes through x-ray binary dynamics.

3. Mass Distribution Analysis

The combined dataset reveals distinct populations:

• Neutron stars cluster between approximately 1.2 and 2.0 solar masses (M⊙), bounded above by the Tolman-Oppenheimer-Volkoff limit.

• Black holes show a lower mass limit around 5 M⊙, with a primary population between 5 and 50 M⊙.

• A potential intermediate population emerges in recent detections, partially filling the traditional "mass gap" between 2 and 5 M⊙.

Higher-mass black holes (above 50 M⊙) appear suppressed, consistent with pair-instability supernova processes that limit progenitor star evolution. These boundaries suggest an equilibrium configuration where physical processes balance to define stable remnant states.

4. Equilibrium Interpretation

In the context of stellar collapse, equilibrium manifests through the balance of gravitational compression against degeneracy pressure (for neutron stars) or event horizon formation (for black holes). The observed mass clustering indicates that remnant formation favors equilibrium states, with minimal variance around physical limits. This structured distribution aligns with TSTOEAO's substrate resolution, where gradients (imbalances in stellar core dynamics) resolve minimally to produce stable outcomes.

5. Implications

The equilibrium envelope in compact object masses provides evidence for unified physical limits across stellar evolution. Future observations may refine these boundaries, testing TSTOEAO predictions for substrate invariance in merger remnants.

Conclusion

Compact object mass distributions from GWTC-4.0 reveal an equilibrium-governed structure, supporting TSTOEAO's unification framework. This analysis demonstrates how observational data at cosmic scales reflect substrate-driven stability.

References:

1. LIGO Scientific Collaboration, Virgo Collaboration, KAGRA Collaboration. (2026). GWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from the First Part of the Fourth LIGO-Virgo-KAGRA Observing Run. arXiv:2508.18082 [gr-qc].

2. LIGO Scientific Collaboration, Virgo Collaboration, KAGRA Collaboration. (2026). GWTC-4.0: An Introduction to Version 4.0 of the Gravitational-Wave Transient Catalog. arXiv:2508.18080 [gr-qc].

3. Swygert, J. (2025). Substrate Signatures: Testable Predictions for O4 Gravitational Waves. tstoeao.com.