Neutron star transition to strong-scalar-field state in tensor scalar gravity

J. Novak

REVIEW

Neutron star transition to strong-scalar-field state in tensor scalar gravity

J. Novak

General Relativity and Quantum Cosmology · Submitted 4 Jun 1998 · 18 references

Pith's verdict: The dynamical transition to scalarization is real and well computed; the energy budget that headlines the abstract is asserted rather than closed, but that softness doesn't sink the central result.

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arXiv IDgr-qc/9806022 (version 1)

Pith IDWN7P5VGY, Pith's permanent record of this paper and its review

CitationJ. Novak. "Neutron star transition to strong-scalar-field state in tensor scalar gravity." arXiv:gr-qc/9806022 (1998). https://pith.science/paper/WN7P5VGY

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Editor's note

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The thing to know: Novak takes the static spontaneous-scalarization picture and actually evolves it. Put a star on the weak-field equilibrium while the two scalarized branches exist, and it falls off that saddle onto one of them, radiating as it goes. That dynamical statement is the new content, and it holds up. The static landscape itself is credited to Damour–Esposito-Farèse and Harada, and Novak reproduces it with four equations of state spanning soft to stiff — that reproduction is a real cross-check, not a formality. The EOS-independence of beta_0^max = -4.34 is a genuinely useful number and the kind of thing people will quote. The waveforms (a ~200 Hz burst, a ~3 kHz ring-down) and the damped-oscillator picture are clean, and the baryon conservation at 10^-5 supports the run's integrity. The quadrupolar section is explicitly an order-of-magnitude estimate built on applying Hartle–Thorne at every timestep of a non-equilibrium evolution; the author says so, and h ~ 10^-12 f^2/d reads as a scaling, which is what it is. No complaint there. Where it's soft is the energy accounting. Three numbers should balance — the static ADM difference between solutions 4 and 5 (6.2e-3 M_sun from Table I), the flux integral of eq. (4.3), and the kinetic functional of eq. (3.1) — and the paper reports each separately, asserts the flux 'corresponds (within errors)' to the static difference, and never shows a time-resolved budget or an error bar on the flux. F(t) is extracted at a single radius, 300 km, with no second-radius convergence check. The quoted 3% code accuracy sits awkwardly beside the 1% final-state agreement in the same paragraph. Eq. (3.1) is admittedly ad hoc, and the author flags that, so the ~10^-5 M_sun kinetic figure is soft. One correction to the reader's framing: the 10^-2 c surface velocity is a direct hydrodynamical output (Fig. 5), not a consequence of eq. (3.1), so the abstract's velocity claim stands on its own. Net: the qualitative claim is robust and cross-checked; the quantitative split is looser than the abstract implies. Worth referee time — this is the paper people will cite for dynamical scalarization, and the energy bookkeeping should be tightened before it settles into the literature.

Referee report

Significance

If the results hold, this is a useful contribution: it converts the static 'spontaneous scalarization' picture of Damour–Esposito-Farèse and Harada into an explicitly computed dynamical transition, and it does so with a code that conserves baryonic mass to 10⁻⁵ and lands within a stated tolerance of the independently computed static strong-field solution. The EOS-independence of β₀^max, checked against four equations of state spanning a broad stiffness range and cross-checked against two prior groups, is a genuinely new and reasonably robust statement. The paper also makes falsifiable statements: monopolar radiation from such transitions is unlikely to be detectable beyond a few hundred kpc, and the quadrupolar channel would require sources within ~10 pc. The qualitative point that the kinetic energy injected during scalarization matters for supernova hydrodynamics is a concrete, checkable prediction for future core-collapse work.

Major objections (4)

[Sec. IV A, Eq. (4.3) and Fig. 10] The headline quantitative claim of the abstract (abstract:s3) is an energy balance: the star 'radiates away the difference in energy between both states (a few 10⁻³ M_⊙c²)'. The manuscript supports this by computing the static ADM difference between solutions 4 and 5 of Table I (1.37807 − 1.37190 = 6.2×10⁻³ M_⊙) and separately integrating the scalar flux, Eq. (4.3), from F(t) extracted at r = 300 km, then asserting agreement 'within errors'. No error bar is ever attached to the flux integral, and no time-resolved budget (dM_ADM/dt plus instantaneous flux) is exhibited. The only accuracy figure quoted for the code is 3% (Sec. III, citing [6]), which is roughly seven times larger than the 0.45% fractional mass difference being resolved. The comparison therefore needs an explicit error budget for E_scal: the extraction-radius dependence of F(t), the finite outer boundary, and the accumulated integration error. Without it, the agreement between the two numbers is asserted rather than demonstrated.
[Sec. III, paragraph 3] The same paragraph states that the final dynamically evolved fields agree with the static code 'within 1% of error (the code indicates 3%, see [6])'. These two numbers are inconsistent as written and the reader cannot tell which applies to the comparison at hand. This matters directly for the energy claim, because the quantity being cross-checked is a 0.45% effect in the mass; a 3% level of agreement in the fields would not discriminate the strong-field endpoint from the weak-field one at the required precision. The accuracy statement should be made unambiguous and, ideally, tied to a convergence study rather than to a citation.
[Sec. III, paragraph 2 and abstract:s2] The abstract and Sec. III state the result in universal form: 'the weak-field state is always unstable when the two other strong-field states exist; these last solutions are both stable.' The evidence displayed is a single evolution (solution 4 of Table I, shown in Figs. 3–10); the generalization rests on the sentence 'Such simulations have been done for various masses and coupling function parameters. Results were very similar', with no table of those runs. Since this is the paper's central claim, a compact table listing, for each run, the EOS, α₀, β₀, baryonic mass, initial solution, final solution reached, and the sign of the final scalar charge would make the universality claim verifiable rather than asserted. The stability classification itself is consistent with Harada's published analyses [11,13], which is fine; the request is for the dynamical evidence to be tabulated.
[Sec. IV B, Eqs. (4.4)–(4.6)] The quadrupolar estimate applies the Hartle–Thorne stationary, axisymmetric perturbation equations at each timestep of a violently non-stationary radial evolution, on the assumption that 'at each time-step of the dynamical integration the star is supposed to be at equilibrium'. The author labels this a 'crude estimate', which is fair, but the domain of validity is never stated: the radial pulsation is at ~3 kHz (Sec. IV A), comparable to or faster than any rotation frequency considered, so the stationarity ordering Ω ≪ Ω_Kepler does not by itself justify the instantaneous application. It would help to state which oscillation amplitude enters the quadrupole, whether the estimate is dominated by the initial transition or by the ringdown, and how the result would change if the star were not assumed to re-equilibrate instantaneously. The detectability conclusion (sources within ~10 pc) inherits this uncertainty and should be flagged as conditional on it.

Minor objections (8)

[Sec. III, Eq. (3.1)] The text following Eq. (3.1) reads 'with Γẽ2 replacing mc²', which appears to be a typesetting corruption; presumably the intended statement is that Γẽ replaces the rest-mass energy density in the particle expression. Please clarify the integrand and its Newtonian limit explicitly.
[Sec. II B, Eq. (2.3)] The value β₀^max = −4.34 ± 0.01 is quoted without saying how the uncertainty was obtained. State whether it reflects the spacing of the β₀ grid, the spread across the four equations of state, or the static code's convergence, since the claim of EOS-independence is one of the paper's main results.
[Table I] Solution 4 has scalar charge ω = −5.91×10⁻² while α₀ = 10⁻², a factor of about six. Sec. II C describes this branch as having a scalar charge 'of the order of α₀'; either soften that phrasing or note the numerical factor, since the distinction between the α₀-ordered and unity-ordered branches is what the paragraph is drawing.
[Sec. IV A] The characteristic frequencies '~200 Hz' for the rapid phase and '~3 kHz' for the damped phase are quoted without saying how they were extracted (period of the dominant oscillation, Fourier transform of F(t), or otherwise). A one-sentence statement of the method would make these numbers reproducible.
[Sec. IV B, Eq. (4.6)] The scaling h^TT ~ 10⁻¹² f²/d does not state the units of d, and the numerical prefactor is not derived in the text. Please give the units explicitly and show the intermediate step from d²Q/dt² ~ 10³² f² kg m² s⁻² to Eq. (4.6).
[Figs. 1 and 2] The captions refer to the scalarization zone lying 'inside solid lines' while also describing a thin dotted line for hydrodynamically unstable configurations; the figures themselves carry two separate 'Spontaneous Scalarization' labels. Please make the caption identify unambiguously which curve is which boundary, and state what the horizontal 2.23 M_⊙ line represents in Fig. 2 where several EOS are overlaid.
[Sec. IV A] The statement that the transition waveform is 'the inverse of that of neutron star collapse to a black hole' is qualitative and would benefit from an explicit pointer to the corresponding figure or equation in [6], so the reader can compare amplitudes directly.
[PACS line] The PACS entry '04.80Cc' is missing its period and should read '04.80.Cc'.

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The paper

The paper claims

A neutron star sitting on the ordinary equilibrium of a tensor-scalar theory is unstable once scalarized solutions exist, and its fall onto one of them converts a few $10^{-3} M_odot c^2$ into monopolar gravitational radiation.

The reading

The paper asks what actually happens to a neutron star on the 'ordinary' branch of solutions in a tensor-scalar theory of gravity once the theory also admits a branch on which the star carries a large scalar charge. Earlier work had shown that such scalarized configurations can exist; Novak's question is whether the ordinary branch is a place a star can really live, or only a knife-edge. Using a spherically symmetric code that solves the coupled Einstein-scalar-fluid equations in time, he finds the ordinary branch is unstable exactly when the two scalarized branches exist, and he follows the resulting transition step by step. If he is right, an accreting neutron star that crosses a critical baryonic mass does not sit still: it lurches into a scalarized configuration, sheds a few $10^{-3} M_odot c^2$ as monopolar scalar radiation, and rings down like a damped oscillator with surface speeds reaching about $10^{-2}c$.

What carries the argument

The load-bearing mechanism is spontaneous scalarization: because the coupling strength between matter and the scalar field depends on the field itself, a sufficiently compact star can lower its energy by acquiring a macroscopic scalar charge, even when the coupling vanishes asymptotically. The paper's version of this is the affine coupling $alpha(phi) = alpha_0 + beta_0(phi - phi_0)$, whose second parameter $beta_0$ controls whether the three-branch structure appears. The dynamical code is a 3+1 radial-gauge, polar-slicing evolution of the Einstein-frame metric, the scalar field, and a perfect fluid, using pseudo-spectral methods sharp enough to resolve an instability and follow it to a new equilibrium. Two secondary devices carry the quantitative claims: the asymptotic expansion $phi(r,t) = phi_0 + F(t - r/c)/r$, which turns the computed field into a detector amplitude $h(t) = (2/d), alpha_0 F(t)$ and a radiated energy $E_{scal} = (c^3/G_*) int (dF/dt)^2 dt$; and the kinetic-energy functional $E_{kin} = int_0^R 4pi Gamma(Gamma - 1) e r^2 dr$, used to apportion the energy gap between radiation and fluid motion.

Extended reading notes

Core claim

For a fixed baryonic mass and a coupling function $alpha(phi) = alpha_0 + beta_0(phi - phi_0)$ with $beta_0$ sufficiently negative, the static equations admit three equilibrium solutions: the usual weak-scalar-field one and two strong-field ones that are mirror images when $alpha_0 = 0$. Novak establishes, by explicit time evolution rather than by a linear stability argument, that the weak-field solution is a local maximum of the energy and is unstable whenever the other two exist, while both strong-field solutions are stable local minima. A star started on the unstable solution undergoes a rapid rearrangement of its matter as the scalar field grows, radiates away the energy difference between the two states as scalar waves, and settles onto one of the scalarized configurations. The radiated energy, integrated from the asymptotic waveform, matches the static energy difference within the code's errors; a small residual, about $10^{-5} M_odot c^2$, appears as oscillating fluid kinetic energy, and the star's surface velocity peaks near $10^{-2}c$. The paper also reports a maximal coupling strength for spontaneous scalarization, $beta_0^{max} = -4.34 pm 0.01$, essentially independent of which of four equations of state is used, and estimates the accompanying quadrupolar emission from a slowly rotating version of the same star as $h^{TT} sim 10^{-12} f^2/d$.

Load-bearing premise

The split of the static energy gap into a radiated scalar flux and a kinetic reservoir inside the star rests on a kinetic-energy integral that the author concedes has no rigorous definition in general relativity, so the quoted $10^{-5} M_odot c^2$ of fluid motion and the $10^{-2}c$ surface velocity are convention-dependent rather than derived quantities.

Editorial extensions

If this is right

An accreting neutron star in a binary that grows past the critical baryonic mass is not a stable endpoint: it must transition to a scalarized state, so the observed population of neutron stars in such a theory should be biased toward the strong-field branch.
The transition is a source of monopolar gravitational radiation whose amplitude is proportional to $alpha_0$; with solar-system bounds on $alpha_0$, the paper concludes such events are undetectable beyond a few hundred kiloparsecs, which rules out the Virgo cluster as a source population.
Because the maximal $beta_0$ allowing scalarization, $-4.34 pm 0.01$, is nearly independent of the equation of state across four models spanning soft to stiff matter, that number functions as a theory-space boundary rather than a statement about dense-matter physics.
The scalarized final states are energetically favored over the weak-field one, so any process that populates the weak-field branch and then compresses the star will release energy in scalar waves rather than conserving it in the star.
The fluid motions excited during the transition also generate quadrupolar radiation at a level independent of $alpha_0$, so a detected quadrupolar signal without a companion monopolar one would constrain the theory from the opposite direction.

Reading between the lines

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

The same instability should operate in a core-collapse setting: a proto-neutron star contracting through the critical compactness would scalarize during the bounce, and the resulting monopolar burst would be coincident with the neutrino signal, giving a timing handle that the accretion scenario lacks.
The paper's claim that the weak-field branch is a local energy maximum suggests a thermodynamic reading: the scalar charge behaves like an order parameter and the transition like a first-order phase change, so one could look for hysteresis, with the reverse transition occurring at a different mass than the forward one.
If the kinetic-energy functional used here misassigns energy, the observable that survives is the asymptotic scalar waveform, since it is read off at large radius; a reanalysis anchored only on the waveform at several extraction radii would be a cleaner test than the internal energy split.
The near-independence of $beta_0^{max}$ from the equation of state hints that the boundary is set by stellar compactness rather than by nuclear physics, which makes it a target for a semi-analytic incompressible-fluid calculation that could confirm or shift the quoted $-4.34$.

Original abstract

Spherical neutron star models are studied within tensor-scalar theories of gravity. Particularly, it is shown that, under some conditions on the second derivative of the coupling function and on star's mass, for a given star there exist two strong-scalar-field solutions as well as the usual weak-field one. This last solution happens to be unstable and a star, becoming massive enough to allow for all three solutions, evolves to reach one of the strong field configurations. This transition is dynamically computed and it appears that the star radiates away the difference in energy between both states (a few $10^{-3} M_\odot c^2$) as gravitational radiation. Since part of the energy ($\sim 10^{-5} M_\odot c^2$) is injected into the star as kinetic energy, the velocity of star's surface can reach up to $10^{-2} c$. The waveform of this monopolar radiation is shown as well as the oscillations undergone by the star. These oscillations are also studied within the slowly-rotating approximation, in order to estimate an order of magnitude of the resulting quadrupolar radiation.

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, 5,673 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.41 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Spherical neutron star models are studied within tensor-scalar theories of gravity. Particularly, it is shown that, under some conditions on the second derivative of the coupling function and on star's mass, for a given star there exist two strong-scalar-field solutions as well as the usual weak-field one. This last solution happens to be unstable and a star, becoming massive enough to allow for all three solutions, evolves to reach one of the strong field configurations. This transition is dynamically computed and it appears that the star radiates away the difference in energy between both states (a few $10^{-3} M_\odot c^2$) as gravitational radiation. Since part of the energy ($\sim 10^{-5} M_\odot c^2$) is injected into the star as kinetic energy, the velocity of star's surface can reach up to $10^{-2} c$. The waveform of this monopolar radiation is shown as well as the oscillations undergone by the star. These oscillations are also studied within the slowly-rotating approximation, in order to estimate an order of magnitude of the resulting quadrupolar radiation.

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	Spherical neutron star models are studied within tensor-scalar theories of gravity.	contribution 0.46	0.76	0.03	asserted 0.88
s1	Particularly, it is shown that, under some conditions on the second derivative of the coupling function and on star's mass, for a given star there exist two strong-scalar-field solutions as well as the usual weak-field one.	result 0.96	0.91	0.44	asserted 0.98
s2	This last solution happens to be unstable and a star, becoming massive enough to allow for all three solutions, evolves to reach one of the strong field configurations.	result 0.90	0.84	0.49	asserted 1.00
s3	This transition is dynamically computed and it appears that the star radiates away the difference in energy between both states (a few $10^{-3} M_\odot c^2$) as gravitational radiation.	result 0.99	0.93	0.28	asserted 0.95
s4	Since part of the energy ($\sim 10^{-5} M_\odot c^2$) is injected into the star as kinetic energy, the velocity of star's surface can reach up to $10^{-2} c$.	result 0.99	0.87	0.07	asserted 0.73
s5	The waveform of this monopolar radiation is shown as well as the oscillations undergone by the star.	result 0.67	0.91	0.05	asserted 1.00
s6	These oscillations are also studied within the slowly-rotating approximation, in order to estimate an order of magnitude of the resulting quadrupolar radiation.	method 0.61	0.89	0.05	asserted 0.88

What kind of paper the classifier reports this is: simulation study 0.79 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

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

Figures

**Figure 1.** FIG. 1. Zone of spontaneous scalarization of general-relat

**Figure 2.** FIG. 2. Same as Fig. 1, but for EOS2, EOS3 and EOS4 (see Sec. II A

**Figure 3.** FIG. 3. Evolution of star’s radius for unstable initial equi

**Figure 4.** FIG. 4. Evolution of star’s central density for unstable ini

**Figure 5.** FIG. 5. Evolution of star’s surface velocity for unstable in

**Figure 6.** FIG. 6. Evolution of star’s central scalar field value for uns

**Figure 7.** FIG. 7. Evolution of star’s kinetic energy defined as

**Figure 8.** FIG. 8. Scalar waveform resulting from the evolution of unst

**Figure 9.** FIG. 9. Scalar waveform resulting from the evolution of unst

**Figure 10.** FIG. 10. Evolution of star’s radiated energy defined in eq.( 4

Figures reproduced from arXiv:gr-qc/9806022 by the authors.

References

Works cited (18)

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J. Novak, Phys. Rev. D 57, 4789 (1998)

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

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C.G. Callan, D. Friedman, E.J. Martinec and M.J. Perry, N ucl. Phys. B 262, 593 (1985)

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T. Damour and A.M. Polyakov, Nucl. Phys. B 423, 532 (1994)

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

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

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E. Gourgoulhon and P. Haensel, Astron. Astrophys. 271, 187 (1993)

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V.R. Pandharipande, Nucl. Phys. A 174, 641 (1971)

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M. Salgado, S. Bonazzola, E. Gourgoulhon and P. Haensel, Astron. Astrophys. 291, 155 (1994)

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T. Harada, Phys. Rev. D 57, 4802 (1998)

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E. Gourgoulhon, P. Haensel and D. Gondek, Astron. Astro phys. 294, 747 (1995)

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J.B. Hartle and K.S. Thorne, Astrophys. J. 153, 807 (1968) 7 −15.0 −13.0 −11.0 −9.0 −7.0 −5.0 −3.0 β0 0.0 0.4 0.8 1.2 1.6 2.0 MB [Msol] Polytrope γ=2.34 Spontaneous Scalarization Spontaneous Scalarization unstable configurations FIG. 1. Zone of spontaneous scalarization of general-relat ivistic neutron star solutions in the baryonic mass ( MB) – β0 plane,...

View on Pith 1968

Forward citations

Cited by 7 Pith papers

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

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.
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.
Scalarization and superradiant instability of black hole induced by dark matter halo in the scalar-tensor theory of gravity
gr-qc 2025-05 unverdicted novelty 5.0 of 10

Black holes with dark matter halos in scalar-tensor gravity exhibit scalarization and superradiant instability in some parameter regions, with halo size and mass affecting outcomes for small halos but coupling constan...
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.

Show 2 more citing papers

Tensor-multi-scalar theories: relativistic stars and 3+1 decomposition
gr-qc 2015-05 conditional novelty 5.0 of 10

In a two-scalar tensor theory, spontaneous scalarization of neutron stars turns on when the coupling eigenvalues beta0 plus or minus beta1 fall below about -4.35, and the target-space curvature radius changes how stro...
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.

How the literature uses it

35 arXiv papers cite this in 64 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 · 49 sentences without a confident label

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
This choice allows for comparisons with Refs. [ref] , where the analysis is entirely carried out in the Einstein frame.

Numerical simulations of stellar collapse in scalar-tensor theories of gravity · Equation of motions · 0.91

Cites it as background 12 papers

As we mentioned before, the dynamical transition to SC have been analyzed by several authors in the past, but in the Einstein frame [ref] where the field is coupled minimally to the curvature but non-minimally to the matter sector.

On the formation of "supermassive" neutron stars and dynamical transition to spontaneous scalarization · Introduction · 0.96
Early studies on the spontaneous scalarization and scalar GW production were concentrated on the massless ST gravity [ref] .

Scalar Gravitational Wave Signals from Core Collapse in Massive Scalar-Tensor Gravity with Triple-Scalar Interactions · Introduction · 0.87
There has been a detailed analysis of the scalar wave signals that emerge from spherically symmetric collapses [ref] , showing the main properties of the scalar waves, which differ greatly from the familiar, and remarkably simple, propagation of tensor waves.

Where is the ringdown? Reconstructing quasinormal modes from dispersive waves · Introduction · 0.92

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] [6]

J. Novak, Phys. Rev. D 57, 4789 (1998)

View on Pith 1998

[2] [1]

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

View on Pith 1992

[3] [2]

C.G. Callan, D. Friedman, E.J. Martinec and M.J. Perry, N ucl. Phys. B 262, 593 (1985)

View on Pith 1985

[4] [3]

T. Damour and A.M. Polyakov, Nucl. Phys. B 423, 532 (1994)

View on Pith 1994

[5] [4]

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

View on Pith 1996

[6] [5]

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

View on Pith 1993

[7] [7]

E. Gourgoulhon and P. Haensel, Astron. Astrophys. 271, 187 (1993)

View on Pith 1993

[8] [8]

V.R. Pandharipande, Nucl. Phys. A 174, 641 (1971)

View on Pith 1971

[9] [9]

M. Salgado, S. Bonazzola, E. Gourgoulhon and P. Haensel, Astron. Astrophys. 291, 155 (1994)

View on Pith 1994

[10] [10]

H.A. Bethe and M.B. Johnson, Nucl. Phys. A 230, 1 (1974)

View on Pith 1974

[11] [11]

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

View on Pith 1997

[12] [12]

R.D. Reasenberg et al., Astrophys. J. 234, L219 (1979); D.S. Robertson, W.E. Carter, and W.H. Dilling er, Nature (London) 349, 768 (1991); D.E. Lebach et al. , Phys. Rev. Lett. 75, 1439 (1995) 6

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