Transition from inspiral to plunge: A complete near-extremal trajectory and associated waveform

Burke, Ollie; Gair, J. R.; Simón, Joan

doi:10.1103/physrevd.101.064026

Cited by 28 publications

(29 citation statements)

References 56 publications

(155 reference statements)

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“…Once the secondary is captured its orbit will decay through gravitational wave emission until it reaches the separatrix and plunges into the massive black hole. Consequently, knowledge of the location of the separatrix is a key ingredient in models of these binaries [4][5][6][7][8][9][10][11]. The region of parameter space near the separatrix is also interesting as it is here that the well known relativistic orbital precession is taken to the extreme, with arbitrary large precession possible when approaching the separatrix [12].…”

Section: Introductionmentioning

confidence: 99%

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Location of the last stable orbit in Kerr spacetime

Stein

Warburton

2020

Phys. Rev. D

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Black hole spacetimes, like the Kerr spacetime, admit both stable and plunging orbits, separated in parameter space by the separatrix. Determining the location of the separatrix is of fundamental interest in understanding black holes, and is of crucial importance for modeling extreme mass-ratio inspirals. Previous numerical approaches to locating the Kerr separatrix were not always efficient or stable across all of parameter space. In this paper we show that the Kerr separatrix is the zero set of a single polynomial in parameter space. This gives two main results. First, we thoroughly analyze special cases (extreme Kerr, polar orbits, etc.), finding strict bounds on the limits of roots, and unifying a number of results in the literature. Second, we pose a stable numerical method which is guaranteed to quickly and robustly converge to the separatrix. This new approach is implemented in the Black Hole Perturbation Toolkit, and results in a ∼ 45× speedup over the prior robust approach. II. TIME-LIKE GEODESICS IN KERR SPACETIMEGiven any spacetime, let us denote the trajectory of a timelike (non-spinning) test body of mass µ by a curve x α (τ ) where τ is the proper time as measured along the world line. The four-velocity of the body is given by arXiv:1912.07609v1 [gr-qc]

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Section: Introductionmentioning

confidence: 99%

“…The upper/lower signs in Eqs. (10) and (11) are to be chosen when the particle is outgoing/ingoing in the radial equation, or downgoing/upgoing in the polar equation. A sign flip occurs in an equation when the particle passes a turning point of the radial or polar motion.…”

Section: Introductionmentioning

confidence: 99%

Location of the last stable orbit in Kerr spacetime

Stein

Warburton

2020

Phys. Rev. D

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“…it follows from eq. (A5) in [46] that ∂ r Ẽ(r isco ) = 0. For moderately rotating primaries and near ISCO, we can expand…”

Section: B Comparison Of Radial Evolution For Moderate and Near-extre...mentioning

confidence: 99%

“…Let us close this discussion with a brief comparison between the analytic results for moderate and nearextremal spins. We write r − risco ∼ δ > η 2/5 , the latter inequality ensuring that we avoid entering the transition region [46,47]. Expanding Eq.…”

Section: B Comparison Of Radial Evolution For Moderate and Near-extre...mentioning

confidence: 99%

Constraining the spin parameter of near-extremal black holes using LISA

Burke,

Gair,

Simón

et al. 2020

Preprint

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We describe a model that generates first order adiabatic EMRI waveforms for quasi-circular equatorial inspirals of compact objects into rapidly rotating (near-extremal) black holes. Using our model, we show that LISA could measure the spin parameter of near-extremal black holes (for a 0.9999) with extraordinary precision, ∼ 3-4 orders of magnitude better than for moderate spins, a ∼ 0.9. Such spin measurements would be one of the tightest measurements of an astrophysical parameter within a gravitational wave context. Our results are primarily based off a Fisher matrix analysis, but are verified using both frequentest and Bayesian techniques. We present analytical arguments that explain these high spin precision measurements. The high precision arises from the spin dependence of the radial inspiral evolution, which is dominated by geodesic properties of the secondary orbit, rather than radiation reaction. High precision measurements are only possible if we observe the exponential damping of the signal that is characteristic of the near-horizon regime of near-extremal inspirals. Our results demonstrate that, if such black holes exist, LISA would be able to successfully identify rapidly rotating black holes up to a = 1 − 10 −9 , far past the Thorne limit of a = 0.998.

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“…2 These features also leave a trace in the dynamics of the transition from inspiral to plunge in a circular equatorial orbit. In [19,20], new potential terms responsible for different scaling behaviours were identified in the near-extremal regime, extending the original analysis by Ori and Thorne [21]. In fact, if near-extremal Kerr black holes exist and are observed, they are predicted to have much higher parameter estimation sensitivity, using gravitational wave probes, than regular rotating Kerr black holes and the origin for such increase can, once more, be traced to the existence of a throat in the near horizon geometry [22].…”

Section: Jhep07(2021)218mentioning

confidence: 99%

Gravitational perturbations from NHEK to Kerr

Castro

Godet

Simón

et al. 2021

J. High Energ. Phys.

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We revisit the spectrum of linear axisymmetric gravitational perturbations of the (near-)extreme Kerr black hole. Our aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. For the near horizon region of the (near-)extreme Kerr solution, i.e. the (near-)NHEK background, we provide a complete characterisation of axisymmetric modes. This involves an infinite tower of propagating modes together with the much subtler low-lying mode sectors that contain the deformations driving the black hole away from extremality. Our analysis includes their effects on the line element, their contributions to Iyer-Wald charges around the NHEK geometry, and how to reconstitute them as gravitational perturbations on Kerr. We present in detail how regularity conditions along the angular variables modify the dynamical properties of the low-lying sector, and in particular their role in the new developments of nearly-AdS2 holography.

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Transition from inspiral to plunge: A complete near-extremal trajectory and associated waveform

Cited by 28 publications

References 56 publications

Location of the last stable orbit in Kerr spacetime

Location of the last stable orbit in Kerr spacetime

Constraining the spin parameter of near-extremal black holes using LISA

Gravitational perturbations from NHEK to Kerr

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