Analytic Solutions of the Teukolsky Equation and Their Low Frequency Expansions

Mano, Shuhei; Suzuki, Hisao; Takasugi, Eiichi

doi:10.1143/ptp.95.1079

Cited by 260 publications

(374 citation statements)

References 12 publications

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“…(6) and (7) in [38]) and [Eqs. (4.1) and (4.9) in [54], evaluated for |s| = 2] denotes the Wronskian of R in and R up . (Note that [21] and [53] denote R in and R up by R H and R ∞ , respectively.)…”

Section: Discussionmentioning

confidence: 99%

“…where ν is the renormalized angular momentum introduced in the MST formalism [54,56]. (Here we denote its dependence on ℓ and m explicitly, which is usually not done in the literature, though we suppress its dependence on R, even though we displayed the analogous dependence on v in [38].)…”

Section: Obtaining Analytic Forms Of the Pn Coefficients Of The mentioning

confidence: 99%

“…(A2) in [24]. This coefficient was derived by Blanchet and Damour in the Appendix of [64] using methods that differ from both the continued fraction method of MST [54] and the monodromy method of Castro et al [62]. We also define…”

Section: Obtaining Analytic Forms Of the Pn Coefficients Of The mentioning

confidence: 99%

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Experimental mathematics meets gravitational self-force

2015

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It is now possible to compute linear in mass-ratio terms in the post-Newtonian (PN) expansion for compact binaries to very high orders using linear black hole perturbation theory applied to various invariants. For instance, a computation of the redshift invariant of a point particle in a circular orbit about a black hole in linear perturbation theory gives the linear-in-mass-ratio portion of the binding energy of a circular binary with arbitrary mass ratio. This binding energy, in turn, encodes the system's conservative dynamics. We give a method for extracting the analytic forms of these post-Newtonian coefficients from high-accuracy numerical data using experimental mathematics techniques, notably an integer relation algorithm. Such methods should be particularly important when the calculations progress to the considerably more difficult case of perturbations of the Kerr metric. As an example, we apply this method to the redshift invariant in Schwarzschild. Here we obtain analytic coefficients to 12.5PN, and higher-order terms in mixed analytic-numerical form to 21.5PN, including analytic forms for the complete 13.5PN coefficient, and all the logarithmic terms at 13PN. We have computed the individual modes to over 5000 digits, of which we use at most 1240 in the present calculation. At these high orders, an individual coefficient can have over 30 terms, including a wide variety of transcendental numbers, when written out in full. We are still able to obtain analytic forms for such coefficients from the numerical data through a careful study of the structure of the expansion. The structure we find also allows us to predict certain "leading logarithm"-type contributions to all orders. The additional terms in the expansion we obtain improve the accuracy of the PN series for the redshift observable, even in the very strongfield regime inside the innermost stable circular orbit, particularly when combined with exponential resummation.

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Section: Discussionmentioning

confidence: 99%

Section: Obtaining Analytic Forms Of the Pn Coefficients Of The mentioning

confidence: 99%

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Experimental mathematics meets gravitational self-force

2015

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“…Bini-Damour work built on Refs. [152][153][154]. b 2PN tidal effects in the conservative dynamics are known explicitly only for circular orbits.…”

Section: Direct Integration Of the Relaxed Einstein Equationsmentioning

confidence: 99%

Sources of Gravitational Waves: Theory and Observations

Buonanno

Sathyaprakash²

2015

General Relativity and Gravitation

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“…The analysis of the analytic structure of the radial Teukolsky equation was first performed by Leaver [25] and further developed by Mano et al [26]; it is this reference to which the reader should refer for a treatment more detailed than the synopsis given here.…”

Section: Radial Teukolsky Functionsmentioning

confidence: 99%

Gravitational radiation from plunging orbits: Perturbative study

Mino

Brink

2008

Phys. Rev. D

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Numerical relativity has recently yielded a plethora of results about kicks from spinning mergers which has, in turn, vastly increased our knowledge about the spin interactions of black hole systems. In this work we use black hole perturbation theory to calculate accurately the gravitational waves emanating from the end of the plunging stage of an extreme mass ratio merger in order to further understand this phenomenon. This study focuses primarily on spin induced effects with emphasis on the maximally spinning limit and the identification of possible causes of generic behavior. We find that gravitational waves emitted during the plunging phase exhibit damped oscillatory behavior, corresponding to a coherent excitation of quasinormal modes by the test particle. This feature is universal in the sense that the frequencies and damping time do not depend on the orbital parameters of the plunging particle. Furthermore, the observed frequencies are distinct from those associated with the usual free quasinormal ringing. Our calculation suggests that a maximum in radiated energy and momentum occurs at spin parameters equal to a=M ¼ 0:86 and a=M ¼ 0:81, respectively, for the plunge stage of a polar orbit. The dependence of linear momentum emission on the angle at which a polar orbit impacts the horizon is quantified. One of the advantages of the perturbation approach adopted here is that insight into the actual mechanism of radiation emission and its relationship to black hole ringing is obtained by carefully identifying the dominant terms in the expansions used.

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Analytic Solutions of the Teukolsky Equation and Their Low Frequency Expansions

Cited by 260 publications

References 12 publications

Experimental mathematics meets gravitational self-force

Experimental mathematics meets gravitational self-force

Sources of Gravitational Waves: Theory and Observations

Gravitational radiation from plunging orbits: Perturbative study

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