Gauge-invariant and coordinate-independent perturbations of stellar collapse: The interior

Gundlach, Carsten; Martín-García, José M.

doi:10.1103/physrevd.61.084024

Cited by 75 publications

(209 citation statements)

References 17 publications

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“…both metric and fluid perturbations, are automatically gauge-invariant. This is due to the fact that the all perturbations conveniently reduce, in the RW gauge, to the corresponding variables arising from a general gauge (coordinate) transformation (see [20] and references therein). The 1st-order perturbed Einstein equations for the case l ≥ 2 reduce to:…”

Section: Formalismmentioning

confidence: 99%

“…These initial data are not meant to represent a realistic physical state of perturbations in the early Universe; they simply allow us to test the method and to extract the physical behavior of perturbations. Regularity conditions determine the variables in the neighbourhood of the origin according to the prescription of [20]. Near r = 0, we require (for all l ≥ 2):…”

Section: Initial and Boundary Conditionsmentioning

confidence: 99%

“…We compare these to cases where Eqs. Equation (19), Equation (20) and Equation (21) are solved retaining terms with no coupling between ϕ and {χ, ς}, that is, by solving the reduced system:φ…”

Section: Coupled Vs Uncoupled Dynamicsmentioning

confidence: 99%

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Evolution of linear perturbations in spherically symmetric dust spacetimes

February¹,

Larena²,

Clarkson³

et al. 2014

Class. Quantum Grav.

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Abstract. We present results from a numerical code implementing a new method to solve the master equations describing the evolution of linear perturbations in a spherically symmetric but inhomogeneous background. This method can be used to simulate several configurations of physical interest, such as relativistic corrections to structure formation, the lensing of gravitational waves and the evolution of perturbations in a cosmological void model. This paper focuses on the latter problem, i.e. structure formation in a Hubble scale void in the linear regime. This is considerably more complicated than linear perturbations of a homogeneous and isotropic background because the inhomogeneous background leads to coupling between density perturbations and rotational modes of the spacetime geometry, as well as gravitational waves. Previous analyses of this problem ignored this coupling in the hope that the approximation does not affect the overall dynamics of structure formation in such models. We show that for a giga-parsec void, the evolution of the density contrast is well approximated by the previously studied decoupled evolution only for very large-scale modes. However, the evolution of the gravitational potentials within the void is inaccurate at more than the 10% level, and is even worse on small scales.

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Section: Formalismmentioning

confidence: 99%

Section: Initial and Boundary Conditionsmentioning

confidence: 99%

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Evolution of linear perturbations in spherically symmetric dust spacetimes

February¹,

Larena²,

Clarkson³

et al. 2014

Class. Quantum Grav.

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show abstract

“…The GWs were extracted using perturbation theory on the spherical background within the Gerlach-Sengupta [23] formalism. More recently, Harada et al [24] have reexamined the axial part of this problem, using null coordinates (HernandezMisner) and a gauge invariant and coordinate independent perturbative formalism developed by Martín-García and Gundlach [25,26,27]. Within this approach Harada et al [24] have been able to follow the spherical collapse of both, supermassive stars and neutron stars, until a black hole forms, computing the GWs that are emitted in the process.…”

Section: Introductionmentioning

confidence: 99%

Accretion-driven gravitational radiation from nonrotating compact objects: Infalling quadrupolar shells

et al. 2004

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This paper reports results from numerical simulations of the gravitational radiation emitted from non-rotating compact objects (both neutron stars and Schwarzschild black holes) as a result of the accretion of matter. We adopt a hybrid procedure in which we evolve numerically, and assuming axisymmetry, the linearized equations describing metric and fluid perturbations coupled to a fully nonlinear hydrodynamics code that calculates the motion of the accreting matter. The initial matter distribution, which is initially at rest, is shaped in the form of extended quadrupolar shells of either dust or obeying a perfect fluid equation of state. Self-gravity of the accreting layers of fluid is neglected, as well as radiation reaction effects. We use this idealized setup in order to understand the qualitative features appearing in the energy spectrum of the gravitational wave emission from compact stars or black holes, subject to accretion processes involving extended objects. A comparison for the case of point-like particles falling radially onto black holes is also provided. Our results show that, when the central object is a black hole, the spectrum is far from having only one clear, monochromatic peak at the frequency of the fundamental quasi-normal mode. On the contrary, it shows a complex pattern, with distinctive interference fringes produced by the interaction between the infalling matter and the underlying perturbed spacetime, in close agreement with results for point-like particles. Remarkably, most of the energy is emitted at frequencies lower than that of the fundamental mode of the black hole. Similar results are obtained for extended shells accreting onto neutron stars, but in this case the contribution of the stellar fundamental mode stands clearly in the energy spectrum. Our analysis illustrates that the gravitational wave signal driven by accretion onto compact objects is influenced more by the details and dynamics of the process, and the external distribution of matter, than by the quasi-normal mode structure of the central object. The gravitational waveforms from such accretion events appear to be much more complex than former simplified assumptions predicted.

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“…For example, its application to a perfect fluid spacetime with a two-parameter equation of state was considered in Ref. [26], including the matching of the fluid perturbations to an exterior spacetime through a moving timelike surface [27].…”

Section: Introductionmentioning

confidence: 99%

Second- and higher-order perturbations of a spherical spacetime

2006

Self Cite

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The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory. The GS harmonics are generalized to an arbitrary number of indices on the unit sphere and a formula is given for their products. The formalism is optimized for its implementation in a computer-algebra system, something that becomes essential in practice given the size and complexity of the equations. All evolution equations for the second-order perturbations, as well as the conservation equations for the energy-momentum tensor at this perturbation order, are given in covariant form, in Regge-Wheeler gauge.

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Gauge-invariant and coordinate-independent perturbations of stellar collapse: The interior

Cited by 75 publications

References 17 publications

Evolution of linear perturbations in spherically symmetric dust spacetimes

Evolution of linear perturbations in spherically symmetric dust spacetimes

Accretion-driven gravitational radiation from nonrotating compact objects: Infalling quadrupolar shells

Second- and higher-order perturbations of a spherical spacetime

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