A toy model for testing finite element methods to simulate extreme-mass-ratio binary systems

Sopuerta, Carlos F.; Sun, Pengtao; Laguna, Pablo; Xu, Jinchao

doi:10.1088/0264-9381/23/1/013

Cited by 28 publications

(44 citation statements)

References 76 publications

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“…It is easy to show, based on Eq. (31), that the two-sided average of F α dir − F α P (with respect to ϕ) vanishes at the limit δx → 0. This, reassuringly, is consistent with our findingL αm = 0.…”

Section: Discussionmentioning

confidence: 96%

“…(59) in entirely analogous to Eq. (31), and the analysis proceeds precisely along the lines of the discussion following the latter Equation, merely replacing P α [5] →P α [5] . The conclusion, as in the scalar case, is thatL αm = 0, and, consequently, we deduce that Eq.…”

Section: Discussionmentioning

confidence: 99%

“…Sopuerta et al proposed the use of finite-element methods for an effective treatment of the particle in 2+1D. This idea was implemented so far only in a 1+1D context [31,32], and it awaits further development. Most recently, Barack and Golbourn [33] proposed a "puncture" scheme (further discussed below) for dealing with the singular behavior of the field in 2+1D.…”

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confidence: 99%

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m-mode regularization scheme for the self-force in Kerr spacetime

2007

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We present a new, simple method for calculating the scalar, electromagnetic, and gravitational self forces acting on particles in orbit around a Kerr black hole. The standard "mode-sum regularization" approach for self-force calculations relies on a decomposition of the full (retarded) perturbation field into multipole modes, followed by the application of a certain mode-by-mode regularization procedure. In recent years several groups have developed numerical codes for calculating black hole perturbations directly in 2+1 dimensions (i.e., decomposing the azimuthal dependence into mmodes, but refraining from a full multipole decomposition). Here we formulate a practical scheme for constructing the self force directly from the 2+1-dimensional m-modes. While the standard mode-sum method is serving well in calculations of the self force in Schwarzschild geometry, the new scheme should allow a more efficient treatment of the Kerr problem.

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Section: Discussionmentioning

confidence: 96%

Section: Discussionmentioning

confidence: 99%

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confidence: 99%

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m-mode regularization scheme for the self-force in Kerr spacetime

2007

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“…The present author and collaborators have been investigating the possibility of using Finite Element methods for this task. First, by studying a toy model in scalar gravity that contains all the ingredients (excepting for the spin of the massive BH) of astrophysical EMRI events [37]. The main conclusion of this numerical experiment was that the use of adaptive techniques for the description of EMRIs can significantly improve the efficiency and accuracy of the numerical computations.…”

Section: Pos(supernova)026mentioning

confidence: 99%

Gravitational Radiation from Neutron Stars and Black Holes

Fernandez-Sopuerta¹

2008

Proceedings of Supernovae: Lights in the Darkness — PoS(SUPERNOVA)

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Gravitational Wave Astronomy is becoming a reality as Earth-based interferometric gravitationalwave detectors reach the design sensitivities and move towards advanced configurations that may lead to gravitational-wave detections in the immediate future. In this contribution, I briefly summarize the basic characteristics of this new area, the discovery prospects and the potential for fundamental physics. Then, I present results of some investigations of two different sources of gravitational waves that are potential targets for present and future planned observatories. First, I will discuss the generation of gravitational radiation by non-linear effects arising from the coupling between radial and non-radial oscillations of neutron stars, which may produce distinctive gravitational-wave signatures. The gravitational radiation emitted by these sources is in the frequency band of Earth-based detectors. And second, I will discuss the gravitational-wave emission during the inspiral of extreme-mass-ratio compact binaries. In this case, the gravitational waves have low frequencies, inside the frequency band of space observatories like LISA.

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“…The most recent of this works has achieved a reasonable accuracy in the far-field solutions, but the method is likely inadequate for accurate determination of the local field near the particle, which is essential for SF calculations. Sopuerta and Laguna [23] suggested the use of finite-element methods for an effective treatment of the particle. This idea (so far implemented for orbits in Schwarzschild [24]) shows much promise, but requires more development.…”

Section: Introductionmentioning

confidence: 99%

Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in2+1dimensions

2007

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We present a new technique for time-domain numerical evolution of the scalar field generated by a pointlike scalar charge orbiting a black hole. Time-domain evolution offers an efficient way for calculating black hole perturbations, especially as input for computations of the local self force acting on orbiting particles. In Kerr geometry, the field equations are not fully separable in the time domain, and one has to tackle them in 2+1 dimensions (two spatial dimensions and time; the azimuthal dependence is still separable). A technical difficulty arises when the source of the field is a pointlike particle, as the 2+1-dimensional perturbation is then singular: Each of the azimuthal modes diverges logarithmically at the particle. To deal with this problem we split the numerical domain into two regions: Inside a thin worldtube surrounding the particle's worldline we solve for a regularized variable, obtained from the full field by subtracting out a suitable "puncture" function, given analytically. Outside this worldtube we solve for the full, original field. The value of the evolution variable is adjusted across the boundary of the worldtube. In this work we demonstrate the applicability of this method in the example of circular orbits around a Schwarzschild black hole (refraining from exploiting the spherical symmetry of the background, and working in 2+1 dimensions).

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A toy model for testing finite element methods to simulate extreme-mass-ratio binary systems

Cited by 28 publications

References 76 publications

m-mode regularization scheme for the self-force in Kerr spacetime

m-mode regularization scheme for the self-force in Kerr spacetime

Gravitational Radiation from Neutron Stars and Black Holes

Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in2+1dimensions

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