Gravitational waves from pulsating stars: Evolving the perturbation equations for a relativistic star

Allen, Gabrielle; Andersson, Nils; Kokkotas, Kostas D.; Schutz, B. F.

doi:10.1103/physrevd.58.124012

Cited by 78 publications

(186 citation statements)

References 39 publications

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“…Finally, we should note that this decomposition is quite similar to the one used by Allen et al [11]. Their variables F and S Allen are related to ours as follows: F = T and S Allen = e 2ν S. In order to avoid numerical problems at the origin, we have to replace K 1 by the following quantity…”

Section: Polar Perturbationsmentioning

confidence: 99%

“…However, we can as well dispense with the fluid equations, since it is possible to eliminate the energy density perturbation δǫ from the evolution equation (11) by virtue of the Hamiltonian constraint (14). In this way we can obtain a consistent system of evolution equations for the metric and extrinsic curvature perturbations alone.…”

Section: The General Formmentioning

confidence: 99%

“…The evolution of polar perturbations of non-rotating stars has been first addressed by Allen et al [11]. In their formulation they describe the oscillations with three coupled wave equations, two for the metric perturbations in and outside the star, and one for the fluid inside the star.…”

Section: Introductionmentioning

confidence: 99%

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New approach to the evolution of neutron star oscillations

Ruoff

2001

Phys. Rev. D

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We present a new derivation of the perturbation equations governing the oscillations of relativistic non-rotating neutron star models using the ADM-formalism. This formulation has the advantage that it immediately yields the evolution equations in a hyperbolic form, which is not the case for the Einstein field equations in their original form. We show that the perturbation equations can always be written in terms of spacetime variables only, regardless of any particular gauge. We demonstrate how to obtain the Regge-Wheeler gauge, by choosing appropriate lapse and shift. In addition, not only the 3-metric but also the extrinsic curvature of the initial slice have to satisfy certain conditions in order to preserve the Regge-Wheeler gauge throughout the evolution. We discuss various forms of the equations and show their relation to the formulation of Allen et al. New results are presented for polytropic equations of state. An interesting phenomenon occurs in very compact stars, where the first ring-down phase in the wave signal corresponds to the first quasinormal mode of an equal mass black hole, rather than to one of the proper quasinormal modes of the stellar model. A somewhat heuristic explanation to account for this phenomenon is given. For realistic equations of state, the numerical evolutions exhibit an instability, which does not occur for polytropic equations of state. We show that this instability is related to the behavior of the sound speed at the neutron drip point. As a remedy, we devise a transformation of the radial coordinate r inside the star, which removes this instability and yields stable evolutions for any chosen numerical resolution.

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Section: Polar Perturbationsmentioning

confidence: 99%

Section: The General Formmentioning

confidence: 99%

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New approach to the evolution of neutron star oscillations

Ruoff

2001

Phys. Rev. D

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“…On the other hand, the late-time dynamics of a massless field reveals nothing of the nature of the central object, which might be extremely diffuse or extremely compact. While the body's internal structure certainly affects the field at early times [7,[9][10][11][12][13][14][15][16][17], the radiative falloff depends only on the asymptotic conditions. The robustness of the inverse power-law decay is well demonstrated in Refs.…”

Section: Radiative Falloff In Spherical Spacetimesmentioning

confidence: 99%

Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

Poisson

2002

Phys. Rev. D

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We consider a massless scalar field propagating in a weakly curved spacetime whose metric is a solution to the linearized Einstein field equations. The spacetime is assumed to be stationary and asymptotically flat, but no other symmetries are imposed -the spacetime can rotate and deviate strongly from spherical symmetry. We prove that the late-time behavior of the scalar field is identical to what it would be in a spherically-symmetric spacetime: it decays in time according to an inverse power-law, with a power determined by the angular profile of the initial wave packet (Price falloff theorem). The field's late-time dynamics is insensitive to the nonspherical aspects of the metric, and it is governed entirely by the spacetime's total gravitational mass; other multipole moments, and in particular the spacetime's total angular momentum, do not enter in the description of the field's late-time behavior. This extended formulation of Price's falloff theorem appears to be at odds with previous studies of radiative decay in the spacetime of a Kerr black hole. We show, however, that the contradiction is only apparent, and that it is largely an artifact of the Boyer-Lindquist coordinates adopted in these studies.

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“…It is, however, convenient because it magnifies the radial axis in a crucial region, and prevents any excessive growth of the radial momentum during the plunge. [Let us mention in passing that the same kind of coordinate has been used in [31] for studying gravitational perturbations of non-rotating relativistic stars. ]…”

Section: Equationsmentioning

confidence: 99%

Final spin of a coalescing black-hole binary: An effective-one-body approach

2007

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We update the analytical estimate of the final spin of a coalescing black-hole binary derived within the Effective-One-Body (EOB) approach. We consider unequal-mass non-spinning blackhole binaries. It is found that a more complete account of relevant physical effects (higher postNewtonian accuracy, ringdown losses) allows the analytical EOB estimate to "converge towards" the recently obtained numerical results within 2%. This agreement illustrates the ability of the EOB approach to capture the essential physics of coalescing black-hole binaries. Our analytical approach allows one to estimate the final spin of the black hole formed by coalescing binaries in a mass range ( ν = m1m2/(m1 + m2) 2 < 0.16) which is not presently covered by numerical simulations.

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Gravitational waves from pulsating stars: Evolving the perturbation equations for a relativistic star

Cited by 78 publications

References 39 publications

New approach to the evolution of neutron star oscillations

New approach to the evolution of neutron star oscillations

Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

Final spin of a coalescing black-hole binary: An effective-one-body approach

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