Neutron stars in scalar-tensor theories of gravity and catastrophe theory

Tomohiro Harada

REVIEW

Neutron stars in scalar-tensor theories of gravity and catastrophe theory

Tomohiro Harada

General Relativity and Quantum Cosmology · Submitted 14 Jan 1998 · 29 references

Pith's verdict: A careful, correctly executed catastrophe-theory classification of scalarized neutron star equilibria; the cusp claim is sound in structure but rests on numerical envelopes shown without resolution or convergence data.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 7 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDgr-qc/9801049 (version 2)

Pith IDWYZPVR34, Pith's permanent record of this paper and its review

CitationTomohiro Harada. "Neutron stars in scalar-tensor theories of gravity and catastrophe theory." arXiv:gr-qc/9801049 (1998). https://pith.science/paper/WYZPVR34

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Quick read on Harada's catastrophe-theory paper. The thing worth knowing: it takes the turning point method into a two-dimensional control space (phi_0, N) and shows that the equilibrium structure of neutron stars in scalar-tensor theory with A(phi) = exp(beta phi^2/2) is a fold catastrophe for beta >~ -4.35 and a cusp catastrophe at phi_0 = 0 for beta <~ -4.35. That classification, plus the structural-stability argument that spontaneous scalarization is not a tuned accident of one coupling function, is the real content. The Landau form itself is credited to Damour and Esposito-Farese, and correctly so; the paper does not pretend otherwise. The ODE system, boundary conditions, matching, and the turning point criteria are all laid out cleanly enough to reimplement, and the local expansions (Eqs. 4.4-4.10, 4.11-4.19) are internally consistent with the drawn bifurcation sets. Credit where due: this is honest, well-organized work, and the near-critical discussion (Figs. 7-8, beta between -4.9 and -4.35) shows the author knows the envelope is delicate there rather than papering over it. He also states plainly that the turning point method alone cannot certify stability, which is why the perturbation anchor in Sec. III is there. On the stress-test note: I think it is right and the reader's weakest_assumption is aimed at the wrong target. A cubic term in omega is removable by translation; the catastrophe type is fixed by the codimension of the degenerate critical point, which is what the envelope geometry encodes. The genuine soft spot is numerical: no grid spacing, no convergence study, no error bars, and a true cusp is hard to distinguish from two nearby folds on a coarse grid. The stronger foundation is sitting right there and unused: A(phi) = exp(beta phi^2/2) is even in phi, so the phi -> -phi symmetry forces the even-in-omega structure and the pitchfork, hence its cusp unfolding, structurally rather than by inspection of Fig. 3. That is a presentational miss, not an error. Minor: the beta thresholds are interpolated from four spot values, and the genericity claim covers coupling functions but not equations of state (one polytrope throughout). None of this breaks the central claim. Who should read it: people working on spontaneous scalarization, binary pulsar constraints on scalar-tensor gravity, and anyone using turning point methods on stellar sequences. It deserves a serious referee, mainly to press on the numerical resolution behind Fig. 3 and to ask for the symmetry argument.

Referee report

Significance

If the classification holds, the paper upgrades spontaneous scalarization from a numerical curiosity of one coupling function to a generic, structurally stable feature of a wide class of scalar-tensor theories, with concrete observational consequences for binary-pulsar constraints and for scalar gravitational-wave emission from collapse or accretion-induced transitions. The strengths are real: the field equations, the polytropic equation of state, the initial conditions, and the matching to the vacuum solution are given explicitly enough to be re-implemented; the stability criteria are stated as operational rules rather than asserted; the local expansions are internally consistent (I checked that Eqs. 4.6 and 4.7 follow from Eq. 4.4, and that Eqs. 4.14 and 4.16 follow from Eq. 4.12, including the factor-of-two asymmetry in the susceptibility across N_a); and the paper makes falsifiable statements, notably omega ~ C^{-1/3} phi_0^{1/3} at N = N_a (Eq. 4.15) and the divergence chi_phi ~ (N_a - N)^{-1} (Eq. 4.16). The appeal to Thom's theorem to argue structural stability against higher-order terms in the exponent of A(phi) is appropriate and correctly used.

Major objections (3)

[Sec. IV B, Eq. (4.11) and Fig. 3] The identification of point a as a cusp point, which is the load-bearing claim of the paper, rests entirely on the shape of the numerically drawn bifurcation set in Fig. 3 and on the pitchfork in Fig. 5. No grid spacing, convergence study, or error estimate is given for the central-density and phi_0 sampling, and a genuine cusp (two branches terminating at a common N_a with phi_0 ~ +/-(N - N_a)^{3/2}) and an avoided crossing of two nearby folds (branches terminating at distinct N_a values) are difficult to distinguish on a coarse grid. The paper's own near-critical discussion for -4.9 <~ beta <~ -4.35 (Figs. 7 and 8), where the number of stable solutions changes as 1, 2, 3, 1, 0 or 1, 2, 3, 2, 0, shows that the envelope is delicate in exactly this regime. A convergence statement near point a, or a demonstration that the two branches meet at a common N_a to within a stated tolerance, is needed to support the cusp classification as a numerical result.
[Sec. IV B, Eq. (4.11)] The justification for omitting the cubic term in omega from Eq. (4.11) is given as 'this catastrophe was classified as the fold type and therefore not the case for point a because of the shape of the bifurcation set seen in Fig. 3.' As written this is circular: the shape of the bifurcation set is precisely what Eq. (4.19) is introduced to predict, so it cannot simultaneously be the evidence for the ansatz that produces Eq. (4.19). The paper has a stronger and non-circular argument available and does not use it: A(phi) = exp(beta phi^2/2) is exactly even in phi, so at phi_0 = 0 the mass function is even in omega, the pitchfork at point a is symmetry-protected, and its two-dimensional unfolding is necessarily the cusp. Invoking this symmetry would make the classification independent of the numerical envelope and would also explain why the two bifurcated branches in Fig. 5 are exactly degenerate rather than accidentally so. I recommend replacing the appeal to Fig. 3 with the symmetry argument, and noting explicitly that a cubic term would in any case be removable by a translation of omega and is therefore not the real content of the ansatz.
[Sec. II and Sec. IV] For a paper whose central result is a numerical classification, the numerical method is under-described. The manuscript does not state the integration scheme or step size used for Eqs. (2.18)-(2.23), the shooting or relaxation procedure by which the surface conditions determine b and d, the tolerance used when matching to the vacuum solution, or how the zeros of the Jacobian in Eq. (3.9) (equivalently the envelopes in Figs. 1 and 3) are located. It also does not state the precision to which the threshold beta ~ -4.35 is determined, even though the fold-versus-cusp dichotomy of the entire paper hinges on which side of that threshold a given beta lies. A short paragraph supplying these details would make the classification reproducible and would let a reader judge whether the near-critical behaviour in Figs. 7 and 8 is physical or resolution-limited.

Minor objections (7)

[Sec. IV B, Figs. 5, 7, 8] The text says the two bifurcated branches are 'degenerate because, for phi_0 = 0, two stable equilibrium solutions are identical except for the sign of the scalar field.' It would be clearer to state that this degeneracy is exact and follows from the phi -> -phi symmetry of A(phi), rather than leaving it to be inferred as a numerical coincidence.
[Sec. IV B] The phrase 'if the system obeys a perfect delay convention' is used without definition. One sentence explaining the convention, and why a physical neutron star accreting or evolving cosmologically should or should not be expected to follow it, would help the reader connect the catastrophe-theory language to the astrophysical scenario.
[Sec. IV B, Eqs. (4.20)-(4.21)] The partial derivative defining alpha_A in Eq. (4.21) should specify what is held fixed; presumably N, but this should be stated, since the same symbol is used for the coupling function alpha(phi) elsewhere.
[Sec. IV B, final paragraph] The statement that 'for beta >~ -4.6, it is the same as that in general relativity' regarding the maximum ADM energy needs clarification. Presumably this means that no scalarized branch exists and the maximum is attained on the general-relativistic sequence, but as written it reads as an unexplained coincidence.
[Sec. V] The suggestion that collapse or an accretion-induced transition would radiate scalar gravitational waves and constitute a candidate source is presented without estimate of amplitude or rate. It should be flagged explicitly as a conjecture rather than a result of the paper.
[References] References [21] and [22] are cited as unpublished (to be published and a preprint, respectively). They are used only for context on boson stars, so this does not affect any claim, but the entries should be updated at proof if the papers have since appeared.
[Sec. III] The authors correctly acknowledge that the turning-point method alone cannot establish stability and anchor the analysis with the perturbation calculation of Eqs. (3.16)-(3.19) at small density. This is handled adequately; I note it only to record that the limitation is recognized and addressed rather than overlooked.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Neutron star equilibrium sequences in scalar-tensor gravity undergo fold catastrophes, and for sufficiently negative coupling strength a cusp catastrophe at zero asymptotic scalar field, which is the same structure as spontaneous scalariz

The reading

The paper asks what happens to the set of stable neutron-star solutions in scalar-tensor gravity when two knobs are turned independently: the star's total baryon number $N$ and the value the scalar field takes far away, $phi_0$. Stability is settled with the turning point method, which says a solution's stability can flip only where the map from the star's central parameters to those two knobs becomes degenerate, which is exactly the bifurcation set of a catastrophe. For the quadratic coupling $A(phi)=exp(frac{1}{2}beta phi^2)$ the answer depends on $beta$: for $beta gtrsim -4.35$ only fold catastrophes occur, while for $beta lesssim -4.35$ a cusp catastrophe appears at $phi_0=0$. The payoff is a classification: spontaneous scalarization of neutron stars is not a numerical curiosity of one tuned coupling function but a structurally stable cusp, so it survives small perturbations of the theory.

What carries the argument

The carrying device is the catastrophe map $chi_m$ from the equilibrium space $M_m={(phi_0,N,omega): partial m/partialomega=0}$ down to the control plane $(phi_0,N)$. Its singular points, where $partial m/partialomega=partial^2m/partialomega^2=0$, project onto a bifurcation set that coincides with the envelope of the numerically drawn curves of constant central density $tilde{rho}_c$. The turning point method (criteria (i) and (ii)) then fixes which branch beyond a crossing is unstable, and Thom's theorem restricts structurally stable catastrophes with two controls to the fold and the cusp, which is what licenses the classification. A Landau-style expansion of the ADM energy in the scalar charge supplies the local normal forms.

Extended reading notes

Core claim

Tracking secularly stable neutron-star equilibria in the two-dimensional control space $(phi_0,N)$, the paper shows that their number and identity reorganize discontinuously as the controls vary. For $beta simeq -4$ the picture is a single fold: one stable solution exists on one side of an envelope in the $(phi_0,N)$ plane and none on the other, and at $phi_0=0$ the surviving branch is exactly the general-relativistic one. For $beta=-6$ the envelope acquires a cusp at $(phi_0,N)=(0,N_a)$: below the critical baryon number the unique stable solution has $omega=0$ and is general-relativistic, while above it the general-relativistic branch becomes unstable and two new stable branches with $omega=pm(D/C)^{1/2}(N-N_a)^{1/2}$ appear, degenerate at $phi_0=0$ and splitting for $phi_0 neq 0$. The local energy $m=frac{C}{4}omega^4-frac{D}{2}(N-N_a)omega^2-phi_0omega+m_a$ yields the cubic equation $partial m/partialomega=0$ whose one-versus-three root structure is the cusp, and gives a scalar susceptibility $chi_phi$ diverging as $|N-N_a|^{-1}$ with a factor-of-two asymmetry between the two sides of the transition.

Load-bearing premise

The cusp identification at the critical point depends on the local energy expansion having no cubic term in the scalar charge, and the paper rules that term out from the visual shape of the numerically computed bifurcation set rather than from a derivation; the passage in question even states that a cubic term would change the number of roots at the critical point, which is the opposite of what the surrounding argument needs, so the symmetric envelope in the figure is doing load-bearing work.

Editorial extensions

If this is right

For $beta gtrsim -4.35$, a neutron star that accretes past the critical baryon number has no stable equilibrium left and must collapse, with the critical mass shifting as $phi_0$ changes.
For $beta lesssim -4.35$ at $phi_0=0$, the general-relativistic branch turns unstable at $N_a$ and the star settles onto one of two mirror branches with opposite scalar charge; the mass changes continuously but its slope in $N$ does not.
Because fold and cusp are the only structurally stable catastrophes with two controls, the qualitative picture is expected to survive small higher-order corrections to the exponent of the coupling function.
The scalar charge and scalar susceptibility near the critical point obey fixed power laws, $omega propto (N-N_a)^{1/2}$ and $chi_phi propto |N-N_a|^{-1}$, giving a template for reading off critical behaviour from numerical scans of other couplings.
If $phi_0$ drifts cosmologically or $N$ grows by accretion, the star can jump between branches and radiate scalar gravitational waves, making branch switching a candidate source for scalar-wave observations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The fold/cusp dichotomy should apply to any stellar family with two independent controls, such as rotating or charged configurations, so it can be used as a cheap consistency check on numerical stability scans rather than as a fact about neutron stars alone.
Because the cusp is generic rather than tuned, observational bounds on $beta$ from binary-pulsar timing are bounds on a structurally stable phenomenon, which makes them harder to evade by small changes to the coupling function.
The factor-of-two asymmetry in $chi_phi$ across $N_a$ is a sharp and inexpensive numerical target: measuring it directly would confirm the quartic Landau form without needing to resolve the whole bifurcation set.
If for some coupling a cubic term in $omega$ is genuinely present, the transition degrades to a fold and the jump between branches becomes discontinuous rather than continuous; mapping which couplings do this would locate where scalarization can be strong.

Original abstract

We investigate neutron stars in scalar-tensor theories. We examine their secular stability against spherically symmetric perturbations by use of a turning point method. For some choices of the coupling function contained in the theories, the number of the stable equilibrium solutions changes and the realized equilibrium may change discontinuously as the asymptotic value of the scalar field or total baryon number is changed continuously. The behaviour of the stable equilibrium solutions is explained by fold and cusp catastrophes. Whether the cusp catastrophe appears or not depends on the choices of the coupling function. These types of the catastrophes are structurally stable. Recently discovered spontaneous scalarization, which is non-perturbative strong-field phenomenon due to the presence of the gravitational scalar field, is well described in terms of the cusp catastrophe.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,463 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.21 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We investigate neutron stars in scalar-tensor theories. We examine their secular stability against spherically symmetric perturbations by use of a turning point method. For some choices of the coupling function contained in the theories, the number of the stable equilibrium solutions changes and the realized equilibrium may change discontinuously as the asymptotic value of the scalar field or total baryon number is changed continuously. The behaviour of the stable equilibrium solutions is explained by fold and cusp catastrophes. Whether the cusp catastrophe appears or not depends on the choices of the coupling function. These types of the catastrophes are structurally stable. Recently discovered spontaneous scalarization, which is non-perturbative strong-field phenomenon due to the presence of the gravitational scalar field, is well described in terms of the cusp catastrophe.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate neutron stars in scalar-tensor theories.	contribution 0.89	0.87	0.03	asserted 0.73
s1	We examine their secular stability against spherically symmetric perturbations by use of a turning point method.	method 0.97	0.93	0.03	asserted 0.96
s2	For some choices of the coupling function contained in the theories, the number of the stable equilibrium solutions changes and the realized equilibrium may change discontinuously as the asymptotic value of the scalar field or total baryon number is changed continuously.	result 1.00	0.82	0.53	hedged possibility 0.58
s3	The behaviour of the stable equilibrium solutions is explained by fold and cusp catastrophes.	interpretation 0.98	0.75	0.35	asserted 1.00
s4	Whether the cusp catastrophe appears or not depends on the choices of the coupling function.	result 0.91	0.74	0.13	asserted 0.99
s5	These types of the catastrophes are structurally stable.	interpretation 0.53	0.50	0.15	asserted 1.00
s6	Recently discovered spontaneous scalarization, which is non-perturbative strong-field phenomenon due to the presence of the gravitational scalar field, is well described in terms of the cusp catastrophe.	interpretation 0.62	0.25	0.25	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 0.52.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (29)

[1]

C. M. Will, Theory and Experiment in Gravitational Physics , revised ed. (Cambridge University Press, Cambridge, Engl and, 1993)

View on Pith 1993
[2]

T. Damour and G. Esposito-Far` ese, Class. Quantum Grav. 9, 2093 (1992)

View on Pith 1992
[3]

C. Brans and R.H. Dicke, Phys. Rev. 124, 925 (1961)

View on Pith 1961
[4]

M.B. Green, J.H. Schwarz, and E. Witten, Superstring Theory, (Cambridge University Press, Cambridge, England, 1987), Vols. 1 and 2

View on Pith 1987
[5]

P.J. Steinhardt and F.S. Accetta, Phys. Rev. Lett. 64, 2740 (1990)

View on Pith 1990
[6]

A. Abramovici et al. , Science, 256, 325 (1992)

View on Pith 1992
[7]

C. Bradaschia et al. . Nucl. Instrum. Methods Phys. Res. A 289, 518 (1990)

View on Pith 1990
[8]

J. Hough, in Proceedings of the Sixth Marcel Grossmann Meeting on Genera l Relativity , Kyoto, Japan, 1991, edited by H. Sato and T. Nakamura (World Scientiﬁc, Singapore, 1992), p. 192

View on Pith 1991
[9]

K. Kuroda et al., in Proceedings of International Conference on Gravitational Waves: Sources and Detectors , Pisa, Italy, , 1996, edited by I. Ciufolini and F. Fidecaro (World Scienti ﬁc, Singapore, 1997), p. 100

View on Pith 1996
[10]

C.M. Will, and H.W. Zaglauer, Astrophys. J. 346, 366 (1989)

View on Pith 1989
[11]

C.M. Will, Phys. Rev. D 50, 6058 (1994)

View on Pith 1994
[12]

M. Shibata, K. Nakao, and T. Nakamura, Phys. Rev. D 50, 7304 (1994)

View on Pith 1994
[13]

M.A. Scheel, S.L. Shapiro, and S.A. Teukolsky, Phys. Re v. D 51, 4208 (1995); 51, 4236 (1995)

View on Pith 1995
[14]

T. Harada, T. Chiba, K. Nakao, and T. Nakamura, Phys. Rev . D 55, 2024 (1997)

View on Pith 1997
[15]

T. Damour and G. Esposito-Far` ese, Phys. Rev. Lett. 70, 2220 (1993)

View on Pith 1993
[16]

T. Damour and G. Esposito-Far` ese, Phys. Rev. D 54, 1474 (1996)

View on Pith 1996
[17]

J. Katz, Mon. Not. R. Astron. Soc., 183, 765 (1978)

View on Pith 1978
[18]

J. Katz, Mon. Not. R. Astron. Soc., 189, 817 (1979)

View on Pith 1979
[19]

R. Sorkin, Astrophys. J. 249, 254 (1981)

View on Pith 1981
[20]

R. Sorkin, Astrophys. J. 257, 847 (1982)

View on Pith 1982
[21]

G.L. Comer and H. Shin-kai, gr-qc/9708071, Class. Quan tum Grav. (to be published)

View on Pith Pith review arXiv
[22]

D.F. Torres, A.R. Liddle, and F.E. Schunk, gr-qc/97100 48

View on Pith
[23]

T. Harada, Prog. Theor. Phys. 98, 359 (1997)

View on Pith 1997
[24]

C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation (Freeman, New York, 1973)

View on Pith 1973
[25]

D.E. Lebach et al. , Phys. Rev. Lett. 75, 1439 (1995)

View on Pith 1995
[26]

J.G. Williams, X.X. Newhall, and J.O. Dickey, Phys. Rev . D 53, 6730 (1996)

View on Pith 1996
[27]

B.K. Harrison, K.S. Thorne, M. Wakano, and J.A. Wheeler , Gravitation Theory and Gravitational Collapse (The University of Chicago Press, Chicago, 1964)

View on Pith 1964
[28]

S. Chandrasekhar, Astrophys. J. 140, 417 (1964)

View on Pith 1964
[29]

T. Damour and A.M. Polyakov, Nucl. Phys. B423, 532 (1994); Gen. Relativ. Gravit. 26, 1171 (1994). 11 FIGURE CAPTION Fig.1. A family of curves of ˜ ρc = const in the ( ϕ0,N ) plane for the β = −4 case. The ordinate is mbN in place of the baryon number N . In region (A), only one stable equilibrium solution exists, while, in regio n (B), no stable equilibri...

View on Pith 1994

Forward citations

Cited by 15 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Missing solutions in scalar-Gauss-Bonnet gravity
gr-qc 2026-11 accept novelty 8.0 of 10

Gapped branches of scalarized neutron stars and a new non-central regularity condition are discovered in scalar-Gauss-Bonnet gravity.
Nature of phase transitions and metastability in scalar-tensor theories
gr-qc 2025-02 conditional novelty 7.0 of 10

In the canonical scalar-tensor scalarization model, the onset of scalarization is a first-order phase transition across most of the parameter space, creating metastable neutron star configurations.
Tidal Love Numbers of Neutron Stars in Horndeski Theories
gr-qc 2025-01 accept novelty 7.0 of 10

In scalar-tensor theories, the 1/r^3 term used to extract neutron star tidal Love numbers contains a Love-number-independent contamination, computed here for minimally coupled and DEF scalar fields.
Novel Observable Signals from First-Order Gravitational Phase Transitions
gr-qc 2026-08 conditional novelty 6.0 of 10

First-order scalarization of a neutron star triggered by accretion emits a long-lived inverse-chirp gravitational breathing mode that is orders of magnitude louder than the continuous second-order case.
Spontaneous scalarization of charged black holes in the Scalar-Vector-Tensor theory
gr-qc 2019-08 conditional novelty 6.0 of 10

Spontaneous scalarization of Reissner-Nordström black holes occurs in the scalar-vector-tensor f4 model, and the resulting scalarized black holes can be overcharged.

Show 10 more citing papers

Relativistic stars in scalar-tensor theories with disformal coupling
gr-qc 2016-04 conditional novelty 6.0 of 10

Disformal coupling between a scalar field and matter suppresses or forbids spontaneous scalarization of neutron stars depending on its sign, and can shift the moment of inertia versus compactness relation away from ge...
Slowly Rotating Anisotropic Neutron Stars in General Relativity and Scalar-Tensor Theory
gr-qc 2014-11 accept novelty 6.0 of 10

Anisotropic pressure in neutron-star cores changes the moment of inertia and lowers the critical scalar-tensor coupling needed for spontaneous scalarization, so binary pulsar data could in principle constrain core anisotropy.
Neutron stars with a generalized Proca hair and spontaneous vectorization
gr-qc 2020-01 conditional novelty 5.0 of 10

Neutron stars in a generalized Proca theory admit vector-field solutions with 0 or 1 nodes depending on the coupling beta, with mass-radius relations that differ from general relativity and from scalar-tensor scalarization.
Scalarized black holes in the presence of the coupling to Gauss-Bonnet gravity
gr-qc 2018-12 conditional novelty 5.0 of 10

Adding a negative quartic term to the quadratic Gauss-Bonnet coupling yields zero-node scalarized black holes whose radial effective potential has no negative region, indicating stability against radial perturbations.
Equatorial Periodic Orbits and Gravitational Wave Phenomenology around Spherically-symmetric vacuum solution in Freund-Nambu scalar-tensor gravity
gr-qc 2026-06 unverdicted novelty 4.0 of 10

Scalar couplings in Freund-Nambu gravity shift ISCO inward and produce detectable temporal dephasing in EMRI gravitational wave bursts while preserving orbit topology.
Optical and orbital characterization of spherically symmetric static black holes of self-gravitating new nonlinear electrodynamics model
gr-qc 2026-03 conditional novelty 4.0 of 10

PINLED Y^n black holes have charge-driven inward shifts of photon sphere, shadow, and ISCO, with null-geodesic observables distinguishing them from RN more clearly than timelike ones.
Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum
astro-ph 2008-06 accept novelty 3.0 of 10

Electromagnetic observations of neutron stars already exclude large regions of scalar-tensor gravity parameter space, while observations near black hole horizons cannot discriminate between theories at all.
Stellar structure models in modified theories of gravity: lessons and challenges
gr-qc 2019-12 accept novelty 2.0 of 10

The review maps how modified gravity changes stellar structure equations and summarizes the resulting constraints from neutron stars and dwarf stars.
Universal Relations and Alternative Gravity Theories
gr-qc 2017-09 conditional novelty 2.0 of 10

Universal relations among neutron star observables (I-Love-Q, higher multipole moments, oscillation frequencies) survive in most alternative theories of gravity, which limits their power to discriminate between theories.
Gravitational Wave Tests of General Relativity with Ground-Based Detectors and Pulsar Timing Arrays
gr-qc 2013-04 conditional novelty 2.0 of 10

Gravitational wave observations of compact binary mergers and pulsar timing can constrain alternatives to general relativity in the strong-field, dynamical regime, and the review catalogues the projected bound for eac...

How later papers used it

57 later papers cite it

Evidence: some. 57 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 8 of the 90 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 1 used its method or tool and 1 cited it as support.

Uses its method or tool 1 of 2 papers with this label

Ensured its neutron star solutions belong to a stable branch following the prescription described in this paper.

Angular momentum sensitivities in scalar-tensor theories (2024) · 0.97 · paraphrased: the licence does not allow quoting

Cites it as support 1 of 2 papers with this label

Combined its finding that the effective scalar coupling differs little between its coupling function and the quadratic model with this paper's structural stability of the quadratic model at the onset of scalarization to conclude that the dependence on the coupling function is small.

Spontaneous Scalarization in Scalar-Tensor Theories with Conformal Symmetry as an Attractor (2021) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

47 arXiv papers cite this in 75 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 53 sentences without a confident label

Uses its method or tool 1 paper

Finally, we also ensure that our neutron star solutions belong to a stable branch following the prescription described in [ref] , i.e. we consider solutions where the following stability criterion is satisfied: [equation]

Angular momentum sensitivities in scalar-tensor theories · Results · 0.97

Uses its data or values 1 paper

This value has previously calculated using a polytropic equation of state to be $-4.35$ in the nonrotating star [ref] and $-3.9$ in rapidly rotating stars [ref] .

Ferromagnetic Neutron Stars in Scalar-Tensor Theories of Gravity · Formalism · 0.91

Compares with it 2 papers

This is in stark contrast to the standard case of scalarized stars in the DEF model and other scalarization theories inspired by it, where the tachyonic instability is eventually quenched, leading to stability [ref] .

Instability of vectorized stars · Conclusions · 0.97
[ref] reached similar conclusions, but worked in the context of catastrophe theory.

Spontaneous scalarization · Linearized dynamics · 1.00

Cites it as support 2 papers

Moreover, using the catastrophe theory, it is shown that the onset of spontaneous scalarization in the quadratic coupling function corresponds to cusp catastrophe [ref] which is structurally stable, i.e. the theory is stable against adding higher order terms in the coupling function.

Spontaneous Scalarization in Scalar-Tensor Theories with Conformal Symmetry as an Attractor · Choice of Coupling Function · 0.98
Detailed investigations of stellar structure [ref] , numerical simulations of collapse [ref] and stability studies [ref] confirmed that spontaneously scalarized configurations would indeed be the end-state of stellar collapse in these theories.

Numerical Relativity and High Energy Physics: Recent Developments · Spontaneous scalarization in compact stars · 0.97

Cites it as background 14 papers

Originally discussed in the context of neutron stars [ref] , it was noted that a tensor-scalar configuration could become nontrivial for a specific range of parameters — the total mass in that particular case.

Scalarization-like mechanism through spacetime anisotropic scaling symmetry · Introduction · 0.92
the scalar field can become tachyonic unstable if $(lnA)_,φφ < 0$, resulting in a NS which supports a nontrivial scalar field configuration [ref] .

Cosmological attractors to general relativity and spontaneous scalarization with disformal coupling · Introduction · 0.81
The properties and stability of scalarized neutron stars have been studied extensively in the literature [ref] .

Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum · Second-order scalar-tensor gravity and radio pulsars · 0.93

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

C. M. Will, Theory and Experiment in Gravitational Physics , revised ed. (Cambridge University Press, Cambridge, Engl and, 1993)

View on Pith 1993

[2] [2]

T. Damour and G. Esposito-Far` ese, Class. Quantum Grav. 9, 2093 (1992)

View on Pith 1992

[3] [3]

C. Brans and R.H. Dicke, Phys. Rev. 124, 925 (1961)

View on Pith 1961

[4] [4]

M.B. Green, J.H. Schwarz, and E. Witten, Superstring Theory, (Cambridge University Press, Cambridge, England, 1987), Vols. 1 and 2

View on Pith 1987

[5] [5]

P.J. Steinhardt and F.S. Accetta, Phys. Rev. Lett. 64, 2740 (1990)

View on Pith 1990

[6] [6]

A. Abramovici et al. , Science, 256, 325 (1992)

View on Pith 1992

[7] [7]

C. Bradaschia et al. . Nucl. Instrum. Methods Phys. Res. A 289, 518 (1990)

View on Pith 1990

[8] [8]

J. Hough, in Proceedings of the Sixth Marcel Grossmann Meeting on Genera l Relativity , Kyoto, Japan, 1991, edited by H. Sato and T. Nakamura (World Scientiﬁc, Singapore, 1992), p. 192

View on Pith 1991

[9] [9]

K. Kuroda et al., in Proceedings of International Conference on Gravitational Waves: Sources and Detectors , Pisa, Italy, , 1996, edited by I. Ciufolini and F. Fidecaro (World Scienti ﬁc, Singapore, 1997), p. 100

View on Pith 1996

[10] [10]

C.M. Will, and H.W. Zaglauer, Astrophys. J. 346, 366 (1989)

View on Pith 1989

[11] [11]

C.M. Will, Phys. Rev. D 50, 6058 (1994)

View on Pith 1994

[12] [12]

M. Shibata, K. Nakao, and T. Nakamura, Phys. Rev. D 50, 7304 (1994)

View on Pith 1994

[13] [13]

M.A. Scheel, S.L. Shapiro, and S.A. Teukolsky, Phys. Re v. D 51, 4208 (1995); 51, 4236 (1995)

View on Pith 1995

[14] [14]

T. Harada, T. Chiba, K. Nakao, and T. Nakamura, Phys. Rev . D 55, 2024 (1997)

View on Pith 1997

[15] [15]

T. Damour and G. Esposito-Far` ese, Phys. Rev. Lett. 70, 2220 (1993)

View on Pith 1993

[16] [16]

T. Damour and G. Esposito-Far` ese, Phys. Rev. D 54, 1474 (1996)

View on Pith 1996

[17] [17]

J. Katz, Mon. Not. R. Astron. Soc., 183, 765 (1978)

View on Pith 1978

[18] [18]

J. Katz, Mon. Not. R. Astron. Soc., 189, 817 (1979)

View on Pith 1979

[19] [19]

R. Sorkin, Astrophys. J. 249, 254 (1981)

View on Pith 1981

[20] [20]

R. Sorkin, Astrophys. J. 257, 847 (1982)

View on Pith 1982

[21] [21]

G.L. Comer and H. Shin-kai, gr-qc/9708071, Class. Quan tum Grav. (to be published)

View on Pith Pith review arXiv

[22] [22]

D.F. Torres, A.R. Liddle, and F.E. Schunk, gr-qc/97100 48

View on Pith

[23] [23]

T. Harada, Prog. Theor. Phys. 98, 359 (1997)

View on Pith 1997

[24] [24]

C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation (Freeman, New York, 1973)

View on Pith 1973

[25] [25]

D.E. Lebach et al. , Phys. Rev. Lett. 75, 1439 (1995)

View on Pith 1995

[26] [26]

J.G. Williams, X.X. Newhall, and J.O. Dickey, Phys. Rev . D 53, 6730 (1996)

View on Pith 1996

[27] [27]

B.K. Harrison, K.S. Thorne, M. Wakano, and J.A. Wheeler , Gravitation Theory and Gravitational Collapse (The University of Chicago Press, Chicago, 1964)

View on Pith 1964

[28] [28]

S. Chandrasekhar, Astrophys. J. 140, 417 (1964)

View on Pith 1964

[29] [29]

T. Damour and A.M. Polyakov, Nucl. Phys. B423, 532 (1994); Gen. Relativ. Gravit. 26, 1171 (1994). 11 FIGURE CAPTION Fig.1. A family of curves of ˜ ρc = const in the ( ϕ0,N ) plane for the β = −4 case. The ordinate is mbN in place of the baryon number N . In region (A), only one stable equilibrium solution exists, while, in regio n (B), no stable equilibri...

View on Pith 1994