Celestial Holes and
Gravitational Wells
Matter Concentration, Interior Gradients, Fragmentation, and the Emergence of Cosmic Structure
John Swygert
October 9, 2026 | Ivory Tower Publishing
Abstract
Celestial bodies are commonly depicted as isolated objects, yet their formation, internal organization, and long-term evolution are inseparable from the gravitational environments in which they occur. This paper develops a deliberately provisional interpretation of planets, stars, brown dwarfs, and larger structures as visible or observable manifestations of gravitationally organized matter. “Celestial hole” names the initial visual analogy; “celestial gravitational well” is adopted as the preferred physical description. A well is not an empty cavity, a black hole, or necessarily a region with a density that increases monotonically toward one point. The paper first distinguishes appearance from measured structure, then examines hydrostatic support, radial concentration, rotation, gravitational collapse, and the routes through which one material environment can yield many bodies. Fragmentation, disk accretion, and collision-driven reassembly are separated explicitly from the unsupported proposition that mature planets routinely divide into descendants. Galaxies require a separate account involving cosmological perturbations, dark-matter halos, baryonic cooling, and feedback. A comparative research protocol then specifies measurable profiles, instability maps, competing formation pathways, falsifiers, and a TSTOEAO-governed inquiry sequence. The result is an explanatory research framework and a set of tests, not a claimed new law of gravity.
Keywords: celestial gravitational well; mass concentration; gravitational potential; radial density; hydrostatic equilibrium; disk instability; fragmentation; accretion; galaxy formation; TSTOEAO.
1. The observational starting point
The Moon, Earth viewed from orbit, and the resolved disks of planets make an immediate impression: a coherent region of luminous or reflecting matter stands out against a much less visually structured background. This is not merely an image invented by the mind. Astronomical bodies are measurable concentrations of mass, and their gravitational influence extends far beyond their visible boundaries. What the eye supplies directly, however, is a projected brightness or color pattern—not a three-dimensional density profile, gravitational potential map, or direct image of spacetime curvature.
The motivating description is of looking inward toward a dynamic center: layered material, circulating clouds or bands, and a surrounding region that appears comparatively quiet. This image is useful as a question generator. It becomes a physical hypothesis only when appearance, kinematics, inferred interior structure, and relativistic effects are treated as different evidentiary categories. In particular, the circular outline of a planet is not evidence that its disk is gravitationally lensing the background. Lensing is inferred through actual deflection, magnification, or time-variable distortion of light from more distant sources. [1]
The central proposal is accordingly modest but substantive: examine the body and its wider gravitational environment as a single evolving system, then determine which measurable relationships organize its concentration, persistence, multiplicity, and eventual transformation.
2. Terminology and limits: from a celestial “hole” to a gravitational well
For scientific discussion, the preferred term in this paper is celestial gravitational well. The original phrase celestial hole is retained in the title and historical motivation only. “Hole” does not imply hollowness, an excavated cavity, a central vacuum, a missing volume of space, an event horizon, or a developmental path toward a black hole. Nor is a gravitational well itself a new category of matter. It is a representation of the gravitational potential generated by an existing mass distribution.
In a weak-field Newtonian model, the potential Φ satisfies Poisson’s equation:
∇²Φ = 4πGρ
Here G is the gravitational constant and ρ is mass density. What is sometimes drawn as a funnel is a diagram of potential, not a literal depression visible through a telescope. The zero point of Φ is conventional; dynamical conclusions depend on spatial differences and gradients. The local gravitational acceleration is g = −∇Φ. In general relativity, curved spacetime rather than a single Newtonian scalar potential supplies the more general description.
A working celestial gravitational well, as used here, is an identified mass distribution and the domain in which its gravitational effects, together with pressure, rotation, transport, and exchange with the environment, shape observable matter or motion. Its boundary must be stated operationally: it might be a material surface, an atmosphere, a chosen enclosed-mass radius, a Hill or tidal region, or a dark-matter halo radius. These are not interchangeable. Some wells contain several important concentrations rather than one neat center.
3. Interior concentration: what gravity predicts and what it does not
For a roughly spherical system, enclosed mass is determined by the radial density distribution:
M(<r) = 4π ∫₀ʳ ρ(s)s² ds
For a nonrotating, hydrostatic sphere, the pressure gradient balances gravity:
dP/dr = − G M(<r)ρ(r) / r²
These standard relations explain why pressure generally rises inward in self-gravitating bodies. They do not require density to rise smoothly, or always to reach its maximum at a geometrical center: density also depends on temperature, composition, phase, and the equation of state. Differentiated rocky planets contain interfaces and discontinuities. Convection can redistribute material. Rapidly rotating bodies are not truly spherical. Interpretations of Jupiter’s gravity data allow a diluted rather than a sharply compact heavy-element core. [2, 3]
Earth supplies an instructive measurement example. Its interior is not established by looking at its illuminated disk: the Preliminary Reference Earth Model reconstructs radial properties from normal modes, seismic travel times, and independent constraints. Such data let investigators distinguish a genuine profile of changing density from an artistic intuition of increasing inward darkness or visual concentration. [2]
For approximately spherical models, an illustrative concentration measure is C₁/₂ = M(<R/2)/M(<R), with R explicitly defined. C₁/₂ is not a universal gravitational law. It is a standardized observable or model-derived summary to be accompanied by uncertainty intervals, density stratification, and selection of the relevant radius. It should not be compared uncritically between a rocky planet, a disk, and a dark-matter halo.
4. Why rotation does not cancel inward assembly
A rotating concentration need not be flung apart. In an approximately circular orbit around a spherical enclosed mass, inward gravity provides the centripetal acceleration required for orbiting:
v²/r ≈ G M(<r)/r²
In a co-rotating description one may speak of centrifugal support; in an inertial description the same orbit is a curved trajectory under gravity. Angular momentum prevents matter from simply falling radially into the center, but it does not eliminate gravitational attraction. Gas can move inward while angular momentum is carried outward through torques, turbulence, magnetic stresses, winds, or other transport. Collapse of rotating gas frequently produces a disk; if its local conditions permit, that disk may generate further condensations.
The actual outcome depends on the budget of gravitational binding, thermal and turbulent support, radiation, magnetic fields, angular momentum transport, tidal forces, and feedback. The instructive question is not “gravity or spinning?” but which terms dominate the local evolution and whether contraction, orbiting, fragmentation, or dispersal follows.
5. Black holes: a comparison, not a hidden assumption
A black hole is not a planet with an especially deep ordinary material center. Its defining feature is an event horizon: a causal boundary from which outward signals cannot escape to distant observers. For an idealized uncharged, nonrotating black hole of mass M, the Schwarzschild radius is:
rₛ = 2GM/c²
This compactness relation does not define ordinary planets, stars, or gravitational wells in general. The classical singularities of idealized relativity are not direct measurements of an interior radial density distribution. An event horizon is therefore a qualitative distinction, not the expected “final stage” of every body. The empirical overlap is that gravity organizes both ordinary astronomical matter and extreme relativistic systems; the governing state of matter and causal geometry can nevertheless differ radically. [4]
6. One concentration, several bodies: separate mechanisms
The biological image of cellular division is an evocative analogy, not an established astronomical mechanism. It must be clarified at the outset: mature planets are not known to reproduce through routine sequential splitting, and there is no evidence for fixed doubling or any other universal multiplication sequence. There are, however, established ways for one initially connected mass reservoir to create several gravitationally organized bodies. [5–8]
6.1 Gravitational fragmentation of a cloud or disk
A molecular cloud can develop multiple collapsing cores; a sufficiently unstable circumstellar disk can also form secondary condensations. ALMA and companion observations of young stellar systems show examples interpreted as disk fragmentation, as distinguished from fragmentation of a larger parent cloud. The units that divide are unstable clouds or disks, not finished adult stars or planets splitting like cells. [5]
For a thin gaseous disk, a commonly used local axisymmetric stability indicator is the Toomre parameter:
Q = cₛκ/(πGΣ)
Here cₛ is sound speed, κ is epicyclic frequency, and Σ is gas surface density. In the idealized thin-disk model, Q below unity indicates local axisymmetric instability. Real disks require attention to thickness, turbulence, magnetic fields, cooling, irradiation, and nonlinear evolution. A map of Q is an instability diagnostic, not a photograph of a planet or proof that a long-lived fragment will form. [6]
6.2 Accretion from a shared reservoir
A protoplanetary disk can yield many bodies through the collective development of solids, planetesimals, embryos, and growing planets. Streaming instabilities, collisions, pebble accretion, and gas acquisition all participate in contemporary formation models. This is “one environment to many objects,” not “one completed object repeatedly divides.” The distinction matters because the mechanisms have different predictions for composition, age, angular momentum, and orbital configuration. [7, 8]
6.3 Disruption and reassembly
Impacts or tides can disrupt material and leave debris that becomes gravitationally bound in a new configuration. A giant-impact family of models is central to current work on the Moon’s origin. Reassembly can produce descendants from common material, but catastrophic disruption has a different energy, debris, and chemical history from smooth cloud fragmentation. [9]
7. Galactic assembly is a change of regime, not planetary fission
A galaxy is not a mature planet that grew, split, and multiplied until a galactic system appeared. Modern cosmological modeling begins with primordial density fluctuations and the growth of structure under gravity, particularly in dark matter. Gas accretes within and along large-scale structures, cools where conditions allow, and forms stars; mergers, outflows, stellar feedback, and black-hole activity may substantially alter that history. The scales, constituent matter, times, and dominant forces differ from those of planetary differentiation or disk planetesimal formation. [10]
Some galaxies host supermassive black holes whose growth interacts with their environments, but an observable black hole is not required as the founding kernel of every gravitational concentration. The physically viable version of a galactic “seed” is usually an initial overdensity and subsequent gravitational halo growth, not an ancestral planet. Continuity exists at the level of gravitational amplification and rearrangement; identity of detailed formation pathways does not follow.
8. WISE 0855: why the illustration inspired a useful question
The October 9, 2026 report concerning WISE 0855 identifies time-variable water-cloud opacity and spectroscopic modulation associated with carbon monoxide and phosphine in an extremely cold brown dwarf. Time-resolved JWST/NIRSpec observations and modeling distinguish changing cloud thickness at relatively low pressures from chemistry tracing deeper atmospheric conditions. The object is thus physically dynamic despite its compact projected appearance. [11, 12]
The widely circulated purple-brown image was explicitly labeled an artist’s concept. It cannot be used as a density map or to claim direct observation of gravitational lensing, a central black hole, or splitting. The actual scientific leverage comes from spectra, temporal modulation, rotation, and atmospheric models. This is an example of why visual intuition can motivate an investigation without serving as the measurements that resolve it.
9. A comparative framework that can fail
A useful research concept must separate systems with different outcomes rather than merely rename all gravitating bodies. Three possible outcomes will be tracked: (A) a persistent, principally single concentration; (B) multiple long-lived concentrations emerging from a shared reservoir; and (C) expansion, stripping, or dispersal that prevents the proposed concentration from persisting. A fourth category, extreme relativistic compactness, requires independent treatment. Outcomes can change with time and are not arranged on a guaranteed ladder of progress.
9.1 Observational levels
Every case should be tagged by evidence class: (i) resolved imagery or brightness; (ii) measured motion, such as orbital velocities and Doppler flows; (iii) inferred interior composition or density from seismic, gravitational, spectral, and equation-of-state constraints; and (iv) genuinely measured relativistic phenomena, including light deflection or gravitational redshift where accessible. Apparent ring shapes and color gradients cannot be promoted to classes (iii) or (iv) without additional measurement. [1, 2]
9.2 Dimensionless measures to test, not assume
Candidate organizing variables include the virial parameter αᵥᵢᵣ ≈ 5σ²R/(GM) for an idealized cloud, Toomre Q for an appropriate disk, a rotation-to-binding measure such as T/|W|, and cooling time relative to the local dynamical time t_cool/t_dyn. Each has physical assumptions, domain limits, and measurement errors; none alone predicts universal multiplication. In a useful comparison, these quantities would be estimated with uncertainties and tested jointly against observed outcomes. [6, 13]
9.3 A pre-registered failure condition
The strong proposal that every body possesses a single ever-denser core, starts with a black-hole seed, or undergoes repeated planetary fission is unsupported and should be rejected if made universal. The weaker description—that gravity organizes concentrations and sometimes multiple bodies—is already standard astrophysics. To claim an additional contribution, a cross-scale classifier or invariant must improve prediction beyond competent domain-specific baselines, on withheld systems and with transparent treatment of uncertainty.
10. A research program using existing data
10.1 Radial density profiles and boundary choices
Build an explicitly labeled set of inferred density and pressure profiles: Earth (seismic inversions and bulk constraints), giant planets (gravity harmonics and interior-model families), brown dwarfs (evolutionary and atmospheric-model constraints), and stars (structure models and, where possible, oscillation constraints). Plot ρ(r)/ρ̄ against r/R within each physically comparable class, report plausible ranges rather than only best-fit curves, and mark layer interfaces. Compare C₁/₂ only after specifying what R and the included mass mean. A finding of divergent or nonmonotonic profiles must be retained, not normalized away. [2, 3]
10.2 Instability maps from disk data
Select observed young disks with spatially resolved gas kinematics and defensible surface-density estimates. Construct Q(r,φ) maps from Σ, κ, and an independently justified thermal or effective sound-speed model; propagate temperature, opacity, abundance, inclination, beam, and mass-conversion uncertainties. Cross-check suspected unstable regions against spiral structure, companions, fragmentation signatures, and estimated cooling times. Publish maps that fail to fragment as prominently as successful cases, to avoid selecting only picturesque examples. [5, 6]
10.3 Discriminating the three one-to-many pathways
For each multiple-body candidate, assess the competing histories of cloud/disk fragmentation, disk accretion, and disruptive reassembly. Use orbital alignment, relative ages, abundance or isotope measurements where available, impact signatures, gas motions, and dynamical reconstruction. These data constrain different causes. A classifier that cannot distinguish at least these pathways has not advanced beyond the original metaphor. [5, 7–9]
10.4 Cross-scale transfer and negative controls
Analyze planetary interiors, star-forming clouds, disks, and galactic halos as separate physical regimes first. Train any proposed dimensionless classifier only within compatible regimes, then test whether an empirically justified transfer rule works out of sample. Include negative controls—non-self-gravitating flows, brightness structures not tracing mass, stabilized disks without fragmentation, and concentrations dispersed by feedback. Compare error rates and prediction calibration with established baseline methods before accepting any “universal” relationship. [10, 13]
11. TSTOEAO as the governing inquiry methodology
TSTOEAO is used here to govern how systems are defined, evidence is gathered, transitions are compared, and proposed relationships are subjected to falsification; it is not used to supersede gravity, hydrodynamics, thermodynamics, or cosmological models. Its methodological sequence is operationalized as Gradient → Boundary → Correction → Cost → Equilibrium, followed by a review of whether the resulting arrangement persists, divides, or disperses.
Gradient: specify measurable spatial or temporal contrasts, such as Φ, ρ, P, temperature, Σ, or velocity shear. Boundary: state exactly how the system and its relevant interface are identified and which fluxes cross it. Correction: identify mechanisms that redistribute material or alter trajectories—pressure gradients, angular-momentum transport, shocks, convection, tides, magnetic processes, and feedback. Cost: measure losses and constraints, including radiative cooling, mechanical work, heating, and mass or energy carried away. Equilibrium: distinguish static hydrostatic balance, rotating quasi-steady states, metastability, and genuinely growing instabilities. Any classification of “persistence” needs an explicitly chosen observation timescale.
The methodological value would be demonstrated if this protocol reduced omitted variables, improved reproducibility, or delivered better out-of-sample classification across appropriate systems. TSTOEAO’s broader formulation, including Encoded Equilibrium and V = E × Y, is not imposed as an astrophysical identity here: E and Y would first require operational units, estimators, and a testable mapping to observables. Treating that equation as a replacement for the field equations would be unjustified. Thus the method governs the inquiry, while measurable physics adjudicates every claim.
12. Interpretation, limitations, and conclusion
The observation that initiated this work should not be dismissed as merely a picture imagined by an observer. The Moon, Earth, planets, and brown dwarfs really are self-gravitating concentrations embedded in extended environments. Greater interior pressures are common, and many bodies have strongly differentiated or concentrated interiors. Rotation, far from disallowing gravitational assembly, participates in making stable or evolving disks, orbits, and multi-body systems. [2, 3, 7]
At the same time, visual brightness is not mass density, a planet’s edge is not the boundary of its gravity, a potential well is not a literal hole, and an ordinary body is not a black hole in miniature. The “one becomes many” intuition has rigorous counterparts in gas fragmentation, shared-reservoir accretion, and debris reassembly; it does not license biological-style division of finished planets. Galaxies demand a distinct dark-matter and cosmological assembly account. [4, 5, 8, 10]
The defensible next claim is therefore conditional and measurable: a gravitationally organized reservoir can remain principally unified, produce several persistent concentrations, or disperse according to the competition among gravity, pressure, transport, dissipation, rotation, tides, and feedback. The central open task is to find whether a reproducible, scale-aware set of diagnostics predicts those alternatives better than existing discipline-specific models. Until that test is performed, “celestial gravitational well” remains a clarifying research description, not an asserted discovery of a new physical mechanism.
References
[1] NASA Science. “Microlensing.” Nancy Grace Roman Space Telescope. https://science.nasa.gov/mission/roman-space-telescope/microlensing/ (accessed October 9, 2026).
[2] Dziewonski, A. M., and D. L. Anderson. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (1981): 297–356. https://doi.org/10.1016/0031-9201(81)90046-7.
[3] Liu, S.-F., et al. “The Formation of Jupiter’s Diluted Core by a Giant Impact.” Nature 572 (2019): 355–357. https://doi.org/10.1038/s41586-019-1470-2. A proposed explanatory model, not a uniquely established formation history.
[4] NASA Science. “Black Holes.” https://science.nasa.gov/universe/black-holes/ (accessed October 9, 2026).
[5] ALMA Observatory. “Young Stellar System Caught in Act of Forming Close Multiples.” October 26, 2016. https://www.almaobservatory.org/en/press-releases/young-stellar-system-caught-in-act-of-forming-close-multiples/.
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[9] NASA Science. “Moon Formation.” https://science.nasa.gov/moon/formation/ (accessed October 9, 2026).
[10] NASA Advanced Supercomputing. “How Many Galaxies Do You Need to Make One Milky Way?” https://nas.nasa.gov/SC21/research/project15.html (accessed October 9, 2026).
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[12] Miles, B. E., et al. “Water Cloud and Chemical Modulations in the Coldest Brown Dwarf.” arXiv:2609.20664, September 17, 2026. https://doi.org/10.48550/arXiv.2609.20664.
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