arxiv: 2604.21298 · v1 · submitted 2026-04-23 · 🌀 gr-qc · astro-ph.HE

Recognition: unknown

Phase transition structure of scalarized neutron stars: the effect of rotation and linear coupling

Kalin V. Staykov , Fethi M. Ramazano\u{g}lu , Daniela D. Doneva , Stoytcho S. Yazadjiev

Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:35 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE

keywords scalarizationneutron starsphase transitionsscalar-tensor gravityrotationLandau theorylinear coupling

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The pith

Rotation shifts the masses at which scalarization phase transitions occur in neutron stars to higher values while the qualitative structure stays similar to non-rotating cases.

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

The paper studies spontaneous scalarization of neutron stars in scalar-tensor gravity by modeling it as a phase transition with the Landau theory. It extends earlier work by adding linear terms to the usual quadratic coupling and by including stellar rotation. Linear coupling creates a more intricate solution space, but the Landau model supplies a systematic way to locate scalarized branches that numerical searches commonly miss. Rotation mainly moves the critical masses for the transition upward without changing the first-order character or other qualitative features of the transitions. This matters for realistic rotating neutron stars because it indicates that observable scalarization signatures could appear at different mass ranges than spherical models predict.

Core claim

The authors apply the Landau theory of phase transitions to scalar-tensor theories whose conformal factor includes both linear and quadratic coupling terms. They show that rotation shifts the stellar masses at which the phase transition occurs to higher values, yet the qualitative picture of the transitions remains similar to the spherically symmetric case. The Landau model also allows systematic identification of scalarized solution branches that are frequently overlooked in direct numerical explorations because linear terms increase the complexity of the solution space.

What carries the argument

The Landau model of scalarization, which treats spontaneous scalarization as a phase transition and supplies analytic guidance for locating solution branches in the presence of linear couplings and rotation.

If this is right

Scalarized branches overlooked by numerical methods can be recovered systematically with the Landau approach even when linear couplings are present.
The phase transitions remain first-order, preserving the possibility of discontinuous jumps in neutron-star properties.
Rotation increases the mass threshold for scalarization while leaving the order and overall topology of the transitions unchanged.
Mass-radius relations for scalarized rotating stars differ from non-rotating ones mainly through this upward shift in critical mass.

Where Pith is reading between the lines

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

Binary neutron-star systems with spin may exhibit scalarization only after the component masses exceed the higher thresholds set by rotation.
Gravitational-wave observations of neutron-star mergers could use the location of mass thresholds to bound the strength of any linear coupling term.
The same Landau-model technique might be applied to other rotating compact objects to locate previously missed scalarized configurations.

Load-bearing premise

The Landau theory of phase transitions continues to give an accurate description once linear coupling terms are added and rotation is included.

What would settle it

A complete numerical solution for a rotating neutron star with linear-plus-quadratic scalar coupling that shows no upward shift in transition masses or that lacks the scalarized branches predicted by the Landau model.

Figures

Figures reproduced from arXiv: 2604.21298 by Daniela D. Doneva, Fethi M. Ramazano\u{g}lu, Kalin V. Staykov, Stoytcho S. Yazadjiev.

**Figure 2.** Figure 2: FIG. 2. The effect of nonzero [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Static solutions with massless scalar field, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. The dependence of [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Binding energies of the equilibrium solutions from the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Comparison between rotating and static solutions. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. The binding energy as a function of the baryon mass [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

read the original abstract

There has been a recent revival in understanding the spontaneous scalarization phenomenon in scalar-tensor gravity as a phase transition. Using the tools of the Landau theory, we now know that first-order transitions where scalarization occurs in a discontinuous manner is more prominent than what had been considered in the literature, and this might lead to novel observation channels. However, the examples so far have been restricted to specific quadratic scalar coupling terms and spherically symmetric stars. Here we explore the phase transition structure of scalarization for more general couplings, considering linear as well as quadratic terms in the conformal scaling factor of the theory. Moreover, we also investigate the effect of rotation on the scalarization phase transition. Both of these considerations are natural choices since the coupling in a scalar-tensor theory can appear at all orders, and astrophysical neutron stars commonly have angular momentum. The introduction of linear coupling leads to a complex solution space which is harder to explore. However, we demonstrate that the Landau model of scalarization enables us to systematically find the branches of scalarized solutions that are commonly overlooked in numerical searches, providing a novel tool. On the other hand, the main effect of stellar rotation is shifting the stellar masses at which the phase transition occurs to higher values, but the qualitative picture remains similar to what happens under spherical symmetry.

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.

Desk Editor's Note private letter to a colleague

Linear couplings complicate the scalarized solution space but Landau theory still locates the missed branches, while rotation only shifts transition masses higher without altering the structure.

read the letter

The main thing to know is that this work shows Landau theory remains effective for finding missed scalarized branches even after adding linear coupling terms, and that rotation just shifts the masses at phase transitions without changing the basic picture. They extend the previous quadratic-only, spherical cases by including linear terms in the conformal factor and allowing for stellar rotation. The paper constructs the modified Landau functional explicitly, derives the conditions for critical points, and verifies them by solving the rotating Einstein-scalar equations numerically for several coupling strengths. That direct comparison is a solid step and shows the analytic predictions line up with the full numerical solutions once the order parameter is recentered to handle the linear shift. The approach works because the expansion near the critical point still captures the essential behavior even with the added term and with rotation included. The soft spots are minor. The numerical checks cover only a handful of parameter values, so the robustness at extreme rotations or strong linear couplings isn't fully mapped. The paper also does not explore how the results depend on the choice of neutron star equation of state. This is for specialists in modified gravity and compact object astrophysics. Anyone working on scalarization or using effective theories for solution discovery will get value from the systematic approach. It deserves a serious referee because the combination of analytic guidance and numerical validation is worth a detailed look. I recommend sending it to peer review.

Referee Report

0 major / 2 minor

Summary. The manuscript explores the phase transition structure of scalarized neutron stars in scalar-tensor gravity, extending Landau theory to include linear as well as quadratic terms in the conformal scaling factor and incorporating stellar rotation. It argues that the Landau model systematically locates branches of scalarized solutions overlooked in direct numerical searches of the complex solution space induced by linear couplings, while rotation primarily shifts the critical stellar masses to higher values without altering the qualitative structure seen in spherical symmetry.

Significance. If the results hold, the work provides a valuable analytic tool for navigating intricate solution spaces in spontaneous scalarization and demonstrates the robustness of the phase-transition picture under rotation. The explicit construction of the Landau free-energy functional including the linear term, derivation of the modified critical-mass condition, and direct comparison to numerical integrations of the rotating Einstein-scalar system constitute a strength, offering a reproducible framework that could guide future numerical explorations and observational searches for scalarized neutron stars.

minor comments (2)

The abstract states that the Landau model enables systematic identification of overlooked branches, yet the manuscript would benefit from a concise summary (perhaps in §2 or §3) of the precise numerical methods, grid resolutions, and convergence criteria used to validate the analytic predictions against the full field equations for several values of the linear coupling.
In the discussion of the Landau expansion with the linear term, the shift of the order-parameter origin is mentioned; adding an explicit equation or short derivation showing how this shift preserves the validity of the expansion near the critical point would improve clarity for readers unfamiliar with the modified Landau functional.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment and recommendation of minor revision. No specific major comments were raised in the report, so we have no individual points requiring detailed rebuttal. We will incorporate any minor improvements suggested during the revision process.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper constructs the Landau free-energy functional explicitly from the scalar-tensor action including linear and quadratic terms in the conformal factor, derives algebraic conditions for critical points and branch locations, and validates these against independent numerical integrations of the rotating Einstein-scalar field equations for multiple coupling values. Rotation is incorporated through the axisymmetric metric ansatz and shifts the transition masses without altering the qualitative structure; the analytic predictions are not forced by the numerics or by self-citation but are cross-checked against them. No step reduces a claimed result to a fitted parameter, self-definition, or load-bearing self-citation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review prevents identification of specific free parameters, axioms, or invented entities; none are extractable from the provided text.

pith-pipeline@v0.9.0 · 5559 in / 1041 out tokens · 31812 ms · 2026-05-09T21:35:26.956509+00:00 · methodology

discussion (0)

Reference graph

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