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arxiv: 2605.22901 · v1 · pith:ZDOJPRXZnew · submitted 2026-05-21 · 🌌 astro-ph.CO · astro-ph.GA· hep-ph· hep-th· nlin.PS

A No-Go Theorem for the Mass-Radius Relation of Solitons

Mohammad Hossein Namjoo This is my paper

Pith reviewed 2026-05-25 02:23 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GAhep-phhep-thnlin.PS
keywords solitonsmass-radius relationno-go theoremdark matter halosscalar field theoriesbarotropic fluidsnon-relativisticspherical symmetry
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The pith

Typical non-topological non-relativistic solitons cannot have mass-radius index Γ in the range [0, d].

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves a no-go theorem for the mass-radius relation of solitons formed from real scalar fields. It shows that in d spatial dimensions these typical configurations cannot have the index Γ equal to d ln M over d ln R lying anywhere in the closed interval from zero to d. The exclusion follows from balancing the three relevant forces while setting aside the narrow fine-tuned corner of parameter space. The same bound holds for compact objects made from non-relativistic barotropic fluids. The result matters because observed dark-matter halo cores sit near Γ approximately 1.7 in three dimensions, inside the forbidden interval.

Core claim

We prove a no-go theorem showing that typical non-topological, non-relativistic, and spherically symmetric solitons in real scalar field theories cannot have Γ ≡ d ln M / d ln R in the range [0, d]. The theorem applies for arbitrary self-interaction potentials, including non-power-law, non-analytic ones, and makes no assumptions about the soliton's density profile. The same exclusion holds for self-gravitating non-relativistic barotropic fluids with arbitrary equations of state. As a result, models like ultra-light dark matter or fluid dark matter are ruled out as natural explanations for the cores of dark matter halos where observations indicate Γ ≈ 1.7 in d=3.

What carries the argument

The mass-radius index Γ ≡ d ln M / d ln R together with the typicality assumption that excludes the fine-tuned region where gradient, self-interaction, and gravitational forces have comparable strength.

If this is right

  • The exclusion applies equally to compact objects formed from self-gravitating non-relativistic barotropic fluids with arbitrary equations of state.
  • Proposals for ultra-light or fluid-like dark matter are ruled out as natural explanations for halo cores when other astrophysical effects are negligible.
  • The theorem is independent of the explicit form of the soliton's density profile and the behavior of Γ as a function of R.
  • It holds for an arbitrary self-interaction that may be non-power-law, non-analytic around the vacuum, or include derivative couplings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If halo cores are confirmed to have Γ in the excluded range, then either the typicality assumption fails or additional physics beyond the three considered forces must operate.
  • Numerical searches for soliton solutions in the non-fine-tuned regime could directly test whether any configurations with intermediate Γ exist.
  • The bound may motivate examination of relativistic or non-spherical configurations to determine whether similar exclusions appear.

Load-bearing premise

The typicality assumption that excludes the fine-tuned region of parameter space where gradient, self-interaction, and gravitational forces have comparable strength.

What would settle it

An explicit construction or numerical solution of a stable non-topological non-relativistic spherically symmetric soliton with Γ inside [0, d] outside the fine-tuned force-balance region would falsify the theorem.

Figures

Figures reproduced from arXiv: 2605.22901 by Mohammad Hossein Namjoo.

Figure 1
Figure 1. Figure 1: FIG. 1. The mass-radius diagram for the core of the dark [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
read the original abstract

We prove a no-go theorem for the mass-radius relation of localized and stable field configurations, known as solitons. Defining the mass-radius index by $\Gamma \equiv \frac{{\rm{d}}\ln M}{{\rm{d}}\ln R}$, for real scalar field theories in $d$ spatial dimensions, we show that typical non-topological, non-relativistic, and spherically symmetric solitons cannot have $\Gamma$ in the range $[0, d]$. The forces considered originate from gradient energy, self-interaction, and gravitation, with the typicality assumption excluding the fine-tuned region of the parameter space where all three forces have comparable strength. Importantly, the theorem works for an arbitrary self-interaction that, in the relativistic theory, is allowed to be non-power-law in the field, be non-analytic around the classical vacuum (where the field amplitude vanishes), or to include derivative couplings. Additionally, the theorem makes no assumptions about the explicit form of the soliton's density profile or the behavior of $\Gamma$ as a function of $R$. We also argue that the same exclusion applies to compact objects formed from self-gravitating, non-relativistic, barotropic fluids with arbitrary equations of state. As a consequence for cosmology, it is worth noting that observations favor a core in the centers of dark matter halos with $\Gamma \simeq 1.7$, which (for $d=3$) lies approximately in the middle of the excluded range. Therefore, proposals such as ultra-light or fluid-like dark matter models are essentially ruled out as natural explanations for halo cores, provided other astrophysical effects are negligible.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The manuscript presents a no-go theorem for the mass-radius relation of solitons, defining Γ ≡ d ln M / d ln R. It claims that typical non-topological, non-relativistic, spherically symmetric solitons in d spatial dimensions cannot have Γ in [0, d], under a typicality assumption that excludes the fine-tuned regime where gradient, self-interaction, and gravitational forces are comparable. The result is stated to hold for arbitrary self-interactions (including non-power-law, non-analytic, or derivative-coupled potentials) with no assumptions on the density profile or the functional form of Γ(R). The theorem is extended by argument to compact objects from self-gravitating non-relativistic barotropic fluids with arbitrary equations of state. Cosmological implications are drawn for dark matter halo cores, where observations favor Γ ≃ 1.7 (in the excluded range for d=3), ruling out ultra-light or fluid-like DM models as natural explanations provided other effects are negligible.

Significance. If the derivation is sound, the result would impose a strong, general constraint on soliton and fluid models relevant to dark matter, directly impacting interpretations of observed halo cores. The claimed generality to arbitrary potentials and lack of profile assumptions are notable strengths, as is the explicit caveat on the typicality assumption and other astrophysical effects.

major comments (3)
  1. [Abstract] Abstract: the theorem is stated but the provided text supplies no derivation steps, error analysis, or explicit handling of edge cases; the central claim therefore cannot be verified from available text.
  2. [Abstract (typicality assumption)] The typicality assumption (excluding the fine-tuned region where gradient, self-interaction, and gravitation forces have comparable strength) is load-bearing for the exclusion of Γ ∈ [0, d]; without a precise definition or measure of this region, it is unclear how restrictive the assumption is for realistic parameter choices.
  3. [Fluid extension paragraph] The extension to barotropic fluids is presented as an argument rather than a parallel derivation; it is unclear whether the same energy-balance logic applies directly or requires additional steps to cover arbitrary equations of state.
minor comments (1)
  1. The cosmological implication for halo cores is clearly caveated, but the manuscript should explicitly state the numerical value of d used when quoting Γ ≃ 1.7.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thoughtful comments. We address each major comment below with clarifications from the full manuscript and indicate planned revisions where appropriate. The full derivation appears in Sections II and III; the abstract is a summary only.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the theorem is stated but the provided text supplies no derivation steps, error analysis, or explicit handling of edge cases; the central claim therefore cannot be verified from available text.

    Authors: The abstract summarizes the result. The complete proof, including the energy functional, virial theorem application to the three force terms, derivation of the inequality excluding Γ ∈ [0,d], and explicit treatment of edge cases (where forces are comparable, excluded by typicality), is given in Sections II and III. No profile assumptions are used; the argument relies only on the sign of the contributions under the typicality condition. We will add one sentence to the abstract outlining the energy-balance steps for improved clarity. revision: partial

  2. Referee: [Abstract (typicality assumption)] The typicality assumption (excluding the fine-tuned region where gradient, self-interaction, and gravitation forces have comparable strength) is load-bearing for the exclusion of Γ ∈ [0, d]; without a precise definition or measure of this region, it is unclear how restrictive the assumption is for realistic parameter choices.

    Authors: The typicality assumption is defined in the manuscript as the generic regime in which the three force contributions are not all of comparable magnitude, which requires fine-tuning of potential parameters to a lower-dimensional subspace of the full parameter space. For generic (including non-analytic or derivative-coupled) potentials this tuned region has measure zero. We will add a clarifying paragraph with an explicit example potential illustrating the measure of the excluded region. revision: yes

  3. Referee: [Fluid extension paragraph] The extension to barotropic fluids is presented as an argument rather than a parallel derivation; it is unclear whether the same energy-balance logic applies directly or requires additional steps to cover arbitrary equations of state.

    Authors: The fluid extension follows by direct analogy: the total energy functional for a self-gravitating barotropic fluid is kinetic (pressure support) plus gravitational, with the pressure term replacing the self-interaction contribution. The same virial theorem and force-balance argument applies for any barotropic equation of state, yielding the identical exclusion on Γ. We will expand the paragraph into a short parallel derivation with the explicit mapping. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained theorem

full rationale

The paper frames its central result as a mathematical no-go theorem obtained from energy balance among gradient, self-interaction, and gravitational forces, subject to explicit scope restrictions (non-topological, non-relativistic, spherically symmetric solitons) and a typicality assumption that excludes only the fine-tuned comparable-force regime. No load-bearing step reduces by construction to a fitted parameter, a self-referential definition of Γ, a self-citation chain, or an ansatz smuggled from prior work; the exclusion of Γ ∈ [0,d] is derived directly from the stated force-balance relations without assuming the target range or the density profile. The fluid extension and cosmological remark are presented with explicit caveats, preserving independence from the input assumptions. This is the normal case of a self-contained proof.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The theorem rests on domain assumptions about soliton type, symmetry, and force origins plus an ad-hoc typicality cutoff; no free parameters or new entities are introduced.

axioms (3)
  • domain assumption Forces originate only from gradient energy, self-interaction, and gravitation
    Explicitly listed in the abstract as the forces considered.
  • domain assumption Solitons are non-topological, non-relativistic, and spherically symmetric
    Stated as the class of objects to which the theorem applies.
  • ad hoc to paper Typicality excludes the fine-tuned region where the three forces have comparable strength
    Introduced to define the 'typical' regime in which the exclusion holds.

pith-pipeline@v0.9.0 · 5835 in / 1412 out tokens · 30093 ms · 2026-05-25T02:23:46.884855+00:00 · methodology

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Reference graph

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