Teukolsky formalism for nonlinear Kerr perturbations

Green, Stephen; Hollands, Stefan; Zimmerman, Peter

doi:10.1088/1361-6382/ab7075

Cited by 45 publications

(39 citation statements)

References 55 publications

(267 reference statements)

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“…On the other hand, the p i and s i terms in the transformation can be deformed in any desirable manner while preserving the ∼ 1/r 2 form of the perturbation at large r. For concreteness, we apply Ξ a as written in Eq. (E.2) for all r, leading to the no-string solution (35), but we keep in mind that only the linear-and-quadratic-in-u terms actually need to be applied globally in this way. components and then expanding the result as a finite power series in ρ whose coefficients are Held scalars.…”

Section: Appendix E Dipole Mode In Flat Spacetimementioning

confidence: 99%

“…In calculating the residual field, however, one is faced with the same challenges encountered earlier in solving the linearized Einstein equation about Kerr-but now with an extended source. Our key insight is that this can be accomplished for h R ab using the "corrector tensor" reconstruction formalism recently developed by Green, Hollands, and Zimmerman [35] (GHZ). Like the CCK procedure, the GHZ procedure begins at the level of Weyl scalars, and reconstructs from these the metric perturbation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New metric reconstruction scheme for gravitational self-force calculations

Toomani

Zimmerman

Spiers

et al. 2021

Class. Quantum Grav.

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Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating the metric perturbation due to a point particle orbiting a Kerr black hole. Currently, the linear perturbation is obtained with a metric reconstruction procedure that puts it in a “no-string” radiation gauge which is singular on a surface surrounding the central black hole. Calculating dynamical quantities in this gauge involves a subtle procedure of “gauge completion” as well as cancellations of very large numbers. The singularities in the gauge also lead to pathological ﬁeld equations at second perturbative order. In this paper we re-analyze the point-particle problem in Kerr using the corrector-ﬁeld reconstruction formalism of Green, Hollands, and Zimmerman (GHZ). We clarify the relationship between the GHZ formalism and previous reconstruction methods, showing that it provides a simple formula for the “gauge completion”. We then use it to develop a new method of computing the metric in a more regular gauge: a Teukolsky puncture scheme. This scheme should ameliorate the problem of large cancellations, and by constructing the linear metric perturbation in a suﬃciently regular gauge, it should provide a ﬁrst step toward second-order self-force calculations in Kerr. Our methods are developed in generality in Kerr, but we illustrate some key ideas and demonstrate our puncture scheme in the simple setting of a static particle in Minkowski spacetime.

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Section: Appendix E Dipole Mode In Flat Spacetimementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New metric reconstruction scheme for gravitational self-force calculations

Toomani

Zimmerman

Spiers

et al. 2021

Class. Quantum Grav.

Self Cite

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show abstract

“…As mentioned above then, the main technical challenge for the second order problem is reconstructing the remaining NP quantities required for the source from only one's knowledge of Ψ (1) 4 . In the remainder of this paper we describe a method for doing so for vacuum perturbations (see [43] for a different reconstruction procedure claimed to also work with gravity coupled to matter that is smooth and of compact support).…”

Section: Perturbations Of Type D Spacetimesmentioning

confidence: 99%

“…There are workarounds to the above mentioned problem (see e.g. [40][41][42][43]), though there are also procedures [36,44] to directly reconstruct the metric from Ψ (1) 4 , which avoid the use of intermediate Hertz potentials. In this work we describe a formalism building on the latter methods, to compute the second order gravitational wave perturbation of an arbitrary Type D spacetime that satisfies the vacuum Einstein equations.…”

Section: Introductionmentioning

confidence: 99%

Second Order Perturbations of Kerr Black Holes: Reconstruction of the Metric

Loutrel,

Ripley,

Giorgi

et al. 2020

Preprint

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Motivated by gravitational wave observations of binary black hole mergers, we present a procedure to compute the leading order nonlinear gravitational wave interactions around a Kerr black hole. We describe the formalism used to derive the equations for second order perturbations. We develop a procedure that allows us to reconstruct the first order metric perturbation solely from knowledge of the solution to the first order Teukolsky equation, without the need of Hertz potentials. Finally, we illustrate this metric reconstruction procedure in the asymptotic limit for the first order quasinormal modes of Kerr. In a companion paper [1] we present a numerical implementation of these ideas.

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“…In this paper we present a method of obtaining the metric perturbation in a more regular gauge: a Teukolsky puncture scheme. The method is an application of the "corrector tensor" reconstruction formalism recently developed by Green, Hollands, and Zimmerman [34] (GHZ). Unlike the CCK procedure, the GHZ procedure can be applied in nonvacuum regions, making it far more flexible.…”

Section: Introductionmentioning

confidence: 99%

New metric reconstruction scheme for gravitational self-force calculations

Toomani,

Zimmerman,

Spiers

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating the metric perturbation due to a point particle orbiting a Kerr black hole. Currently, the linear perturbation is obtained with a metric reconstruction procedure that puts it in a "no-string" radiation gauge which is singular on a surface surrounding the central black hole. Calculating dynamical quantities in this gauge involves a subtle procedure of "gauge completion" as well as cancellations of very large numbers. The singularities in the gauge also lead to pathological field equations at second perturbative order. In this paper we re-analyze the point-particle problem in Kerr using the corrector-field reconstruction formalism of Green, Hollands, and Zimmerman (GHZ). We clarify the relationship between the GHZ formalism and previous reconstruction methods, showing that it provides a simple formula for the "gauge completion". We then use it to develop a new method of computing the metric in a more regular gauge: a Teukolsky puncture scheme. This scheme should ameliorate the problem of large cancellations, and by constructing the linear metric perturbation in a sufficiently regular gauge, it should provide a first step toward second-order selfforce calculations in Kerr. Our methods are developed in generality in Kerr, but we illustrate some key ideas and demonstrate our puncture scheme in the simple setting of a static particle in Minkowski spacetime.

show abstract

Teukolsky formalism for nonlinear Kerr perturbations

Cited by 45 publications

References 55 publications

New metric reconstruction scheme for gravitational self-force calculations

New metric reconstruction scheme for gravitational self-force calculations

Second Order Perturbations of Kerr Black Holes: Reconstruction of the Metric

New metric reconstruction scheme for gravitational self-force calculations

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