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arxiv: 2605.17078 · v1 · pith:WPSZRX5Onew · submitted 2026-05-16 · 🌀 gr-qc

Boson Stars surrounded by Polish Doughnuts in Scalar-Tensor Theory

Kristian Gjorgjieski , Maxim Rose , Burkhard Kleihaus , Jutta Kunz , Petya Nedkova This is my paper

Pith reviewed 2026-05-20 14:56 UTC · model grok-4.3

classification 🌀 gr-qc
keywords boson starsscalar-tensor theoryPolish doughnutsaccretion disksspontaneous scalarizationrotating solutionsdisk morphologystrong-field gravity
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The pith

Scalarized boson stars allow accretion disks to reach the center and form two-centered cusped shapes.

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

The paper examines thick accretion disks around rotating self-interacting boson stars in general relativity and scalar-tensor theories, with focus on spontaneously scalarized solutions. It shows that scalarization changes the spacetime so that innermost circular orbits often disappear, permitting stable motion inward to the center and producing highly compact quasi-spherical disks. For the heaviest scalarized stars a non-monotonic angular momentum distribution further supports two-centered disks joined by a cusp. These disks prove more compact and more strongly bound than their general-relativistic counterparts, suggesting possible observational markers of alternative gravity.

Core claim

Scalarization induces qualitative changes in the spacetime that significantly affect disk morphology. In particular, scalarized boson stars can lack innermost circular orbits, allowing stable motion down to the center and enabling highly compact, quasi-spherical disks. For the most massive scalarized solutions, a non-monotonic angular momentum profile further permits two-centered disk configurations connected by a cusp. Overall, disks around scalarized boson stars are more compact and more strongly bound than those in general relativity.

What carries the argument

Spontaneously scalarized rotating self-interacting boson star solutions in scalar-tensor theory, which reshape the effective spacetime geometry and angular-momentum distribution felt by surrounding constant-specific-angular-momentum fluid disks.

Load-bearing premise

The analysis assumes equilibrium models with constant specific angular momentum and a particular self-interacting scalar potential that permits spontaneous scalarization.

What would settle it

Numerical evolution or high-resolution observation of a disk around a boson-star candidate that always terminates at an innermost circular orbit and shows only single-centered morphology without cusps would falsify the reported qualitative changes.

Figures

Figures reproduced from arXiv: 2605.17078 by Burkhard Kleihaus, Jutta Kunz, Kristian Gjorgjieski, Maxim Rose, Petya Nedkova.

Figure 1
Figure 1. Figure 1: Rotating boson stars: (a) shows the binding energy versus the scaled boson mass of the GR [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) showcases the location of the ICO over the angular frequency in terms of the circum [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) ℓ ± K distribution for the energetically preferred solutions. The black curve marks the transition from GR to STT solutions. (b) lower limit ℓS of the disk specific angular momentum up to which static orbits and thus static surfaces exist within disk solutions, plotted over the mass. The range is then given by ℓ0 ∈ (ℓS, 0). The dashed vertical line marks the transition from GR to STT. (c) binding energ… view at source ↗
Figure 4
Figure 4. Figure 4: Equatorial effective potential for different prograde disk solutions for the picked GR and [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) cross section plot of the disk effective potential with [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) range of ℓ0 for which two-centered disks exist for the most massive STT boson stars, illustrated by the shaded area. (b) exemplary cross section plot for a two-centered disk around the STT boson star with M = 5.163 with ℓ0 = −5.252M. The solid vertical lines mark the inner and outer center, the dotted vertical line marks the location of the cusp. The colored horizontal curve marks the equi-potential su… view at source ↗
read the original abstract

We investigate thick accretion disks (Polish Doughnuts) around rotating self-interacting boson stars in general relativity and scalar-tensor theories, focusing on spontaneously scalarized solutions and their general relativistic counterparts. Using equilibrium models with constant specific angular momentum, we analyze disk structures across the parameter space, with emphasis on the phase transition between GR and scalarized configurations. We find that scalarization induces qualitative changes in the spacetime that significantly affect disk morphology. In particular, scalarized boson stars can lack innermost circular orbits, allowing stable motion down to the center and enabling highly compact, quasi-spherical disks. For the most massive scalarized solutions, a non-monotonic angular momentum profile further permits two-centered disk configurations connected by a cusp. Overall, disks around scalarized boson stars are more compact and more strongly bound than those in general relativity, highlighting distinctive features that may serve as observational signatures of alternative gravity theories in the strong-field regime.

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

2 major / 2 minor

Summary. The manuscript investigates thick accretion disks modeled as Polish Doughnuts around rotating self-interacting boson stars in general relativity and scalar-tensor theories, with emphasis on spontaneously scalarized solutions and their GR counterparts. Using equilibrium models with constant specific angular momentum, the authors analyze disk structures across parameter space and report a phase transition between GR and scalarized configurations. Key results include the absence of innermost circular orbits in scalarized spacetimes, enabling stable motion to the center and highly compact quasi-spherical disks; for the most massive scalarized solutions, non-monotonic angular momentum profiles permit two-centered disk configurations connected by a cusp. Disks around scalarized boson stars are found to be more compact and more strongly bound than those in GR, potentially serving as observational signatures of modified gravity.

Significance. If the results hold, the work identifies qualitative differences in accretion disk morphology between GR and scalar-tensor theories that could provide strong-field observational discriminants, particularly through the lack of ISCOs and the emergence of cusp-connected multi-centered structures. The emphasis on equilibrium models with explicit parameter choices allows direct comparison of GR and scalarized cases.

major comments (2)
  1. [Abstract] Abstract: the reported two-centered cusped configurations and extreme compactness rely on equilibrium models constructed with strictly constant specific angular momentum. The central claim that scalarization induces qualitatively distinct disk morphologies (absent in GR) would be undermined if these features do not persist under modest radial variations in l, as expected for viscous or magnetized disks. The manuscript should test the robustness of the non-monotonic l(r) profiles and cusp equilibria by constructing at least a subset of models with non-constant angular momentum distributions.
  2. [Methods] Numerical construction of solutions: the abstract presents clear qualitative results on phase transitions and disk morphologies, yet no quantitative error estimates, convergence tests with respect to grid resolution, or cross-checks against independent codes are mentioned. Without these in the methods, it is impossible to judge whether the reported absence of ISCOs and the non-monotonic angular momentum profiles are numerically robust or sensitive to discretization choices.
minor comments (2)
  1. [Figures] Figure captions should explicitly label the locations of the cusp and the two density maxima in the two-centered configurations to aid reader interpretation.
  2. [Introduction] Notation for the scalar self-interaction parameters should be defined once in the text and used consistently; currently the abstract refers to them without prior introduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address each major comment in detail below, explaining our position and indicating the revisions we intend to implement.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the reported two-centered cusped configurations and extreme compactness rely on equilibrium models constructed with strictly constant specific angular momentum. The central claim that scalarization induces qualitatively distinct disk morphologies (absent in GR) would be undermined if these features do not persist under modest radial variations in l, as expected for viscous or magnetized disks. The manuscript should test the robustness of the non-monotonic l(r) profiles and cusp equilibria by constructing at least a subset of models with non-constant angular momentum distributions.

    Authors: We appreciate the referee highlighting the reliance on constant specific angular momentum. This choice follows the standard Polish Doughnut construction, where constant l permits closed equipotential surfaces via the effective potential method. The non-monotonic angular momentum profiles we report are those of circular geodesics in the scalarized spacetime itself; this non-monotonicity is a geometric feature induced by scalarization and enables a single constant-l value to support multiple centers or cusps. Because the underlying effective potential is determined by the metric, we expect the qualitative distinctions (including the possibility of two-centered structures) to remain robust under modest radial variations in the fluid angular momentum distribution. Nevertheless, we will add a dedicated discussion paragraph in the revised manuscript that explicitly addresses the constant-l approximation, explains why the spacetime-driven features should persist for slowly varying l, and acknowledges that a full parameter study with non-constant distributions lies beyond the present equilibrium analysis. revision: partial

  2. Referee: [Methods] Numerical construction of solutions: the abstract presents clear qualitative results on phase transitions and disk morphologies, yet no quantitative error estimates, convergence tests with respect to grid resolution, or cross-checks against independent codes are mentioned. Without these in the methods, it is impossible to judge whether the reported absence of ISCOs and the non-monotonic angular momentum profiles are numerically robust or sensitive to discretization choices.

    Authors: We agree that quantitative assessments of numerical accuracy should be provided. In the revised manuscript we will expand the Methods section to include (i) explicit error estimates for the metric and fluid quantities, (ii) convergence tests performed at multiple grid resolutions, and (iii) any cross-checks against known analytic limits or independent numerical implementations used during code development. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results derive from independent numerical solutions of field equations

full rationale

The paper numerically solves the coupled Einstein-scalar field equations for rotating boson stars in scalar-tensor theory, then constructs equilibrium Polish Doughnut models with constant specific angular momentum on the resulting metrics. Reported features such as absence of ISCOs, non-monotonic circular-orbit angular momentum profiles, and resulting disk morphologies (including two-centered cusped configurations) are direct outputs of these solutions rather than quantities defined in terms of themselves or fitted parameters. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain. The analysis remains self-contained against external numerical benchmarks and the stated assumptions.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The work relies on the existence of spontaneously scalarized solutions for a chosen self-interacting potential and on the validity of the constant-specific-angular-momentum assumption for thick disks; no new particles or forces are postulated beyond the scalar field already present in scalar-tensor theory.

free parameters (2)
  • constant specific angular momentum l
    Chosen by hand for each equilibrium sequence; controls disk size and shape.
  • scalar self-interaction parameters
    Fixed to values that permit spontaneous scalarization; not derived from first principles.
axioms (2)
  • standard math The spacetime admits a Killing vector and the disk is stationary and axisymmetric.
    Standard assumption for constructing equilibrium configurations in GR and scalar-tensor theories.
  • domain assumption The scalar field is minimally coupled with a specific quartic self-interaction potential that triggers spontaneous scalarization.
    Required for the existence of the scalarized branch studied in the paper.

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