Informational-Field-Assisted Formation of Early Massive Black Holes

The discovery of massive black holes within the first billion years of cosmic history presents an important challenge for understanding how black-hole seeds formed and evolved. Observations of GN-z11 at redshift 10.6, the UHZ1 candidate near redshift 10.3, and the little-red-dot population constrain early black-hole formation but do not uniquely establish a single origin mechanism. Conventional explanations involving direct-collapse heavy seeds, stellar remnants, dense clusters, dark-sector processes, and rapid or super-Eddington accretion remain viable.

This revised paper develops a falsifiable alternative: informational-field-assisted massive black-hole seeding, motivated by the Unified Informational Physics Ontology (UIPO) and formulated within conventional covariant Einstein-Klein-Gordon theory.

The model introduces a minimally coupled complex scalar field with explicit stress-energy, allowing self-gravitating condensates to form under suitable physical conditions. Unlike the original 2025 formulation, it does not equate a dimensionless informational measure with spacetime curvature or invoke informational time as an additional source of cosmic age or black-hole growth.

For the free-field benchmark, the established Kaup stability relation,

M_K = 0.633 M_Pl²/m_I,

connects scalar-particle mass to a characteristic maximum condensate mass. Using the unreduced Planck mass, a benchmark scalar mass of approximately 8.46 × 10⁻¹⁶ eV corresponds to a compact-object mass scale of approximately 10⁵ solar masses. If sufficiently massive condensates develop in early cosmological environments and undergo gravitational collapse, they could produce heavy black-hole seeds without introducing an artificial mass-creation mechanism.

Subsequent evolution follows standard accretion physics. A 10⁵-solar-mass seed formed by redshift 20 requires an effective time-averaged Eddington ratio multiplied by duty cycle of approximately 0.54 to reach the estimated GN-z11 black-hole mass by redshift 10.6.

The November 2026 revision extends the original theoretical model through seven quantitative research areas:

1. Covariant stress-energy conservation and corrected Planck-mass normalization.

2. Scalar-field cosmological abundance and necessary density constraints.

3. Halo mass, condensation efficiency, and the minimum conditions for seed formation.

4. Collapse efficiency and its consequences for subsequent black-hole growth.

5. Particle-mass constraints and scalar–black-hole coupling.

6. Black-hole seed-mass distributions, population predictions, and model distinguishability.

7. Cosmological timing, accretion requirements, and competing growth histories.

The analysis establishes additional quantitative bounds, limiting cases, and falsification conditions. It also identifies an important observational degeneracy: substantially different initial seed masses can produce the same observed black-hole mass under different permitted accretion histories. Consequently, reproducing the mass of an early black hole is not sufficient to identify its formation mechanism.

The revised research introduces a population-level comparison framework, synthetic mass-function calculations, likelihood-based testing procedures, and explicit conditions under which conventional or alternative seed models would outperform the proposed scalar-condensate hypothesis.

The central scientific result remains conditional. The field equations, benchmark relationships, and derived constraints are mathematically specified and computationally reproducible. However, the work does not establish that the proposed scalar field exists, that the required condensates form with sufficient cosmological abundance, or that their collapse produces the observed black-hole population.

The hypothesis can be rejected if independent calculations exclude the relevant parameter space, if cosmological simulations fail to produce sufficient early condensates, if nonlinear evolution favors dispersion over black-hole formation, or if competing models explain the observations without a distinctive contribution from the proposed mechanism.

Reproducibility Package — Version 2.0

The accompanying reproducibility package includes executable Python calculations, frozen model parameters, generated numerical outputs, automated tests, and verification documentation. Ten automated tests passed, covering the principal analytic and synthetic calculations.

The package reproduces the scalar-mass mapping, cosmological timing, halo and abundance constraints, collapse-efficiency sensitivities, particle-coupling calculations, population-model examples, and accretion benchmarks. It does not substitute for cosmological field simulations, numerical-relativity collapse calculations, or independent observational validation.

Scientific Significance

If independently supported, the proposed mechanism would provide an additional parameter-linked formation channel for massive black-hole seeds during cosmic dawn. Its potential significance lies not merely in reproducing early black-hole masses, but in generating testable population predictions capable of distinguishing scalar-condensate seeding from established baryonic and dark-sector alternatives.

Future research priorities include cosmological scalar-field simulations, nonlinear collapse modeling, independently constrained seed-mass distributions, host-galaxy correlations, gravitational-wave signatures, and comparative analysis using consistently selected observational datasets.