Erratum: “Kludge” gravitational waveforms for a test-body orbiting a Kerr black hole [Phys. Rev. D<b>75</b>, 024005 (2007)]

Babak, S.; Fang, Hua; Gair, J. R.; Glampedakis, Kostas; Hughes, Scott A.

doi:10.1103/physrevd.77.049902

Cited by 95 publications

(134 citation statements)

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“…In particular, these methods will allow us to extract the secular part of the evolution of both the orbital constants of the motion and the phase constants, from self-force calculations. It is straightforward to include secular changes to the orbital parameters in the kludge framework [13] and by doing this it should be possible to ensure that the kludge waveform stays in phase with the true waveform for long stretches of the inspiral. It will be important to have accurate but cheap to calculate waveform models available when the data from GW detectors is analysed, as this data analysis will rely heavily on matched-filtering using template waveforms.…”

Section: Discussionmentioning

confidence: 99%

“…The numerical kludge waveform for EMRIs is a fast and accurate way to compute the long waveforms [13] that will be needed for EMRI data analysis. These are built in a not entirely consistent way, but the basic philosophy is to model the underlying trajectory of the inspiralling object as accurately as possible in order to obtain the best possible phase match between the true and approximate waveforms.…”

Section: B Numerical "Kludge" Waveformmentioning

confidence: 99%

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Forced motion near black holes

et al. 2011

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We present two methods for integrating forced geodesic equations in the Kerr spacetime. The methods can accommodate arbitrary forces. As a test case, we compute inspirals caused by a simple drag force, mimicking motion in the presence of gas. We verify that both methods give the same results for this simple force. We find that drag generally causes eccentricity to increase throughout the inspiral. This is a relativistic effect qualitatively opposite to what is seen in gravitationalradiation-driven inspirals, and similar to what others have observed in hydrodynamic simulations of gaseous binaries. We provide an analytic explanation by deriving the leading order relativistic correction to the Newtonian dynamics. If observed, an increasing eccentricity would thus provide clear evidence that the inspiral was occurring in a non-vacuum environment.Our two methods are especially useful for evolving orbits in the adiabatic regime. Both use the method of osculating orbits, in which each point on the orbit is characterized by the parameters of the geodesic with the same instantaneous position and velocity. Both methods describe the orbit in terms of the geodesic energy, axial angular momentum, Carter constant, azimuthal phase, and two angular variables that increase monotonically and are relativistic generalizations of the eccentric anomaly. The two methods differ in their treatment of the orbital phases and the representation of the force. In the first method, the geodesic phase and phase constant are evolved together as a single orbital phase parameter, and the force is expressed in terms of its components on the Kinnersley orthonormal tetrad. In the second method, the phase constants of the geodesic motion are evolved separately and the force is expressed in terms of its Boyer-Lindquist components. This second approach is a direct generalization of earlier work by Pound and Poisson [1] for planar forces in a Schwarzschild background.

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Section: Discussionmentioning

confidence: 99%

Section: B Numerical "Kludge" Waveformmentioning

confidence: 99%

Forced motion near black holes

et al. 2011

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“…As a result, EMRI waveforms serve as highly precise probes of strong gravity and of the spacetime around rotating SMBHs. Considerable study has been devoted to astrophysical scenarios for EMRIs [1][2][3] as well as to the analysis of their waveforms [4][5][6][7][8][9][10].…”

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confidence: 99%

Effect of massive perturbers on extreme mass-ratio inspiral waveforms

2011

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Extreme mass ratio inspirals, in which a stellar-mass object orbits a supermassive black hole, are prime sources for space-based gravitational wave detectors because they will facilitate tests of strong gravity and probe the spacetime around rotating compact objects. In the last few years of such inspirals, the total phase is in the millions of radians and details of the waveforms are sensitive to small perturbations. We show that one potentially detectable perturbation is the presence of a second supermassive black hole within a few tenths of a parsec. The acceleration produced by the perturber on the extreme mass-ratio system produces a steady drift that causes the waveform to deviate systematically from that of an isolated system. If the perturber is a few tenths of a parsec from the extreme-mass ratio system (plausible in as many as a few percent of cases) higher derivatives of motion might also be detectable. In that case, the mass and distance of the perturber can be derived independently, which would allow a new probe of merger dynamics.

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“…But such trigonometric terms are found, usually in a product withS, in the general evolution equations (i.e. ˜ / , / , Q/ , and ι/ ) published in the literature [24,29,31]. One may use Eqs.…”

Section: Directional Derivatives In The˜ − Planementioning

confidence: 99%

“…Theoretical models to describe the orbital evolution of the secondary object in various situations have been derived and presented in the literature: circular orbits in the equatorial plane of the primary object [1][2][3][4][5][6], elliptical orbits in the equatorial plane [7][8][9][10][11][12][13], and an extensive body of research on circular or elliptical orbits inclined with respect to the equatorial plane [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Such models are used to generate hypothetical gravitational waveforms (GW), which provide templates for use in the detection of gravitation wave signals by pattern recognition (Punturo et al [32]).…”

Section: Introductionmentioning

confidence: 99%

The Carter constant for inclined orbits about a massive Kerr black hole: near-circular, near-polar orbits

Komorowski¹,

Valluri²,

Houde³

2012

Open Physics

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Abstract:In an extreme mass-ratio binary black hole system, a non-equatorial orbit will list (i.e. increase its angle of inclination, ι) as it evolves in Kerr spacetime. The abutment, a set of evolving, near-polar, retrograde orbits, for which the instantaneous Carter constant (Q) is at its maximum value (Q X ) for given values of latus rectum (˜ ) and eccentricity ( ), has been introduced as a laboratory in which the consistency of Q/ with corresponding evolution equations for ˜ / and / might be tested independently of a specific radiation back-reaction model. To demonstrate the use of the abutment as such a laboratory, a derivation of Q/ , based only on published formulae for ˜ / and / , was performed for elliptical orbits on the abutment. The resulting expression for Q/ matched the published result to the second order in . We believe the abutment is a potentially useful tool for improving the accuracy of evolution equations to higher orders of and˜ −1 . PACS (2008):

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Erratum: “Kludge” gravitational waveforms for a test-body orbiting a Kerr black hole [Phys. Rev. D75, 024005 (2007)]

Cited by 95 publications

References 0 publications

Forced motion near black holes

Forced motion near black holes

Effect of massive perturbers on extreme mass-ratio inspiral waveforms

The Carter constant for inclined orbits about a massive Kerr black hole: near-circular, near-polar orbits

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