Astroseismology of neutron stars from gravitational waves in the limit of perfect measurement

Suvorov, Arthur G.

doi:10.1093/mnras/sty1080

Cited by 9 publications

(9 citation statements)

References 69 publications

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“…Now we want to make some remarks regarding the possible application of the RZ metric in the inverse spectrum problem, where one reconstructs the perturbation potentials or metric from a given quasi-normal mode spectrum, e.g. [47][48][49][50][51]. An important question in this problem is the uniqueness of the reconstructed potential.…”

Section: Discussionmentioning

confidence: 99%

Scalar fields and parametrized spherically symmetric black holes: Can one hear the shape of space-time?

Völkel

Kokkotas

2019

Phys. Rev. D

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In this work we study whether parametrized spherically symmetric black hole solutions in metric theories of gravity can appear to be isospectral when studying perturbations. From a theory agnostic point of view, the test scalar field wave equation is the ideal starting point to approach the quasinormal mode spectrum in alternative black hole solutions. We use a parametrization for the metric proposed by Rezzolla and Zhidenko, as well as the the higher order WKB method in the determination of the quasi-normal mode spectra. We look for possible degeneracies in a tractable subset of the parameter space with respect to the Schwarzschild quasi-normal modes. Considering the frequencies and damping times of the expected observationally most relevant quasi-normal modes, we find such degeneracies. We explicitly demonstrate that the leading Schwarzschild quasi-normal modes can be approximated by alternative black hole solutions when their mass is treated as free parameter. In practice, we conclude that the mass has to be known with extremely high precision in order to restrict the leading terms in the metric expansion to currently known limits coming from the PPN expansion. Possible limitations of using the quasi-normal mode ringdown to investigate black hole space-times are being discussed.

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Section: Discussionmentioning

confidence: 99%

Scalar fields and parametrized spherically symmetric black holes: Can one hear the shape of space-time?

Völkel

Kokkotas

2019

Phys. Rev. D

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“…Even more interesting are the implications of our results for the inverse spectrum problem. The new Bohr-Sommerfeld rule can be inverted to reconstruct approximatively the perturbation potential from a known spectrum and potentially be used to determine the equation of state throughout the star [67]. This approach requires the knowledge of many modes.…”

Section: Discussionmentioning

confidence: 99%

“…As it was pointed out recently in [67], knowing the perturbation potential can be used to determine the equation of state and solve the inverse problem for the stellar structure. The here presented methods allows a simple, but approximate reconstruction of the potential.…”

Section: Reconstruction Of the Potentialmentioning

confidence: 99%

On the inverse spectrum problem of neutron stars

Völkel

Kokkotas

2019

Class. Quantum Grav.

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In this work we revisit axial perturbations of spherically symmetric and non-rotating neutron stars. Although it has been object of many studies, it still offers new insights that are of potential interest for more realistic scenarios or in the study exotic compact objects, which have drawn much attention recently. By using WKB theory, we first derive a new Bohr-Sommerfeld rule that allows to investigate the quasi-normal mode spectrum and address the inverse spectrum problem. The pure analytical treatment of the wave equation is rather involved, because it requires the solution of the TOV equations and the non-trivial tortoise coordinate transformation depending on the underlying space-time. Therefore we provide an easy way to construct potentials that simplifies the analytical treatment, but still captures the relevant physics. The approximated potential can be used for calculations of the axial perturbation spectrum. These results are also useful in the treatment of the inverse problem. We demonstrate this by reconstructing the time-time component of the metric throughout the star and constraining the equation of state in the central region. Our method also provides an analytical explanation of the empirically known asteroseismology relation that connects the fundamental QNM and radius of a neutron star with its compactness.

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“…Consider any two stars, characterised by two distinct metrics of the form (10), where the first star has radius R 1 , and the second has radius R 2 . Without loss of generality, assume that R 2 ≥ R 1 .…”

Section: A Spherically Symmetric Starsmentioning

confidence: 99%

A metric on the space of neutron star models in general relativity and modified gravity

Suvorov

2020

Class. Quantum Grav.

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Intuitively, some pairs of neutron star models can be thought of as being 'closer' together than others, in the sense that more precise observations might be required to distinguish between them than would be necessary for other pairs. In this paper, borrowing ideas from the study of geometrodynamics, we introduce a mathematical formalism to define a geometric distance between stellar models, to provide a quantitative meaning for this notion of 'closeness'. In particular, it is known that the set of all Riemannian metrics on a manifold itself admits the structure of a Riemannian manifold ('configuration manifold'), which comes equipped with a canonical metric. By thinking of a stationary star as being a particular 3 + 1 metric, the structure of which is determined through the Tolman-Oppenheimer-Volkoff relations and their generalisations, points on a suitably restricted configuration manifold can be thought of as representing different stars, and distances between these points can be computed. We develop the necessary mathematical machinery to build the configuration manifold of neutron star models, and provide some worked examples to illustrate how this space might be used in future studies of neutron star structure.

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Astroseismology of neutron stars from gravitational waves in the limit of perfect measurement

Cited by 9 publications

References 69 publications

Scalar fields and parametrized spherically symmetric black holes: Can one hear the shape of space-time?

Scalar fields and parametrized spherically symmetric black holes: Can one hear the shape of space-time?

On the inverse spectrum problem of neutron stars

A metric on the space of neutron star models in general relativity and modified gravity

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