Computational Methods for the Self-Force in Black Hole Spacetimes

Barack, Leor

doi:10.1007/978-90-481-3015-3_12

Cited by 4 publications

(8 citation statements)

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“…In this section we investigate how well does the post-Newtonian expansion compare with another very important approximation scheme in general relativity: The gravitational self-force approach, based on black-hole perturbation theory, which gives an accurate description of extreme mass ratio binaries having q ≪ 1 or equivalently ν ≪ 1, even in the strong field regime. The gravitational self-force analysis [317, 360, 178, 231] (see [348, 177, 23] for reviews) is thus expected to provide templates for extreme mass ratio inspirals (EMRI) anticipated to be present in the bandwidth of space-based detectors.…”

Section: Conservative Dynamics Of Compact Binariesmentioning

confidence: 99%

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Blanchet

2014

Living Rev. Relativ.

1,428

1,617

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To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries — binary star systems composed of neutron stars and/or black holes in their late stage of evolution — require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary’s orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries — moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.

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Section: Conservative Dynamics Of Compact Binariesmentioning

confidence: 99%

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Blanchet

2014

Living Rev. Relativ.

1,428

1,617

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“…where F is any smooth function representing a time derivative of the quadrupole moment, and Q denotes the Legendre function of the second kind. 23 Note that there is no need to include a finite part operation FP in Eq. ( 83) as the integral is convergent.…”

Section: Gravitational-wave Tails and Tails-of-tailsmentioning

confidence: 99%

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Blanchet

2013

Preprint

122

238

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To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries -binary star systems composed of neutron stars and/or black holes in their late stage of evolution -require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational selfforce for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary's orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries -moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.

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“…Evaluating F requires computing (or retrieving from a cache) the 2-D puncture field and effective source. 31 We have considered a number of possible choices for precisely which terms from the main evolution equation (2.40) should be treated implicitly (i.e., put into G). 31 Unfortunately, in all IMEX schemes of which we are aware it is not the case that there are repeated evaluations of F with different state vectors at the same time coordinate, so there is no reuse possible of the puncture field and effective source from one evaluation to the next.…”

Section: Implicit-explicit (Imex) Evolution Schemesmentioning

confidence: 99%

“…31 We have considered a number of possible choices for precisely which terms from the main evolution equation (2.40) should be treated implicitly (i.e., put into G). 31 Unfortunately, in all IMEX schemes of which we are aware it is not the case that there are repeated evaluations of F with different state vectors at the same time coordinate, so there is no reuse possible of the puncture field and effective source from one evaluation to the next. In contrast (as noted in section IV B 2), with the classical RK4 scheme 50% of evaluations are repeated in this way, so -since the effective source computation dominates the code's overall running time -there is an easy factor-of-two saving in computational cost by caching and reusing the effective source from one evaluation to the next if the evaluation time is unchanged.…”

Section: Implicit-explicit (Imex) Evolution Schemesmentioning

confidence: 99%

“…The O(µ) "MiSaTaQuWa" equations of motion for a gravitational point particle in a (strong-field) curved spacetime were first derived by Mino, Sasaki, and Tanaka [24] and Quinn and Wald [25] (also see Detweiler's analysis [26]) and have recently been rederived in a more rigorous manner by Gralla and Wald [27]. 5 See [21,[29][30][31][32][33][34][35] for general reviews of gravitational radiationreaction dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime

Thornburg

Wardell

2017

Phys. Rev. D

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If a small "particle" of mass µM (with µ ≪ 1) orbits a black hole of mass M , the leadingorder radiation-reaction effect is an O(µ 2 ) "self-force" acting on the particle, with a corresponding O(µ) "self-acceleration" of the particle away from a geodesic. Such "extreme-mass-ratio inspiral" systems are likely to be important gravitational-wave sources for future space-based gravitationalwave detectors. Here we consider the "toy model" problem of computing the self-force for a scalarfield particle on a bound eccentric orbit in Kerr spacetime. We use the Barack-Golbourn-Vega-Detweiler effective-source regularization with a 4th order puncture field, followed by an e imφ ("mmode") Fourier decomposition and a separate time-domain numerical evolution in 2+1 dimensions for each m. We introduce a finite worldtube that surrounds the particle worldline and define our evolution equations in a piecewise manner so that the effective source is only used within the worldtube. Viewed as a spatial region, the worldtube moves to follow the particle's orbital motion. We use slices of constant Boyer-Lindquist time in the region of the particle's motion, deformed to be asymptotically hyperboloidal and compactified near the horizon and J + . Our numerical evolution uses Berger-Oliger mesh refinement with 4th order finite differencing in space and time. Our computational scheme allows computation for highly eccentric orbits and should be generalizable to orbital evolution in the future. Our present implementation is restricted to equatorial geodesic orbits, but this restriction is not fundamental. We present numerical results for a number of test cases with orbital eccentricities as high as 0.98. In some cases we find large oscillations ("wiggles") in the self-force on the outgoing leg of the orbit shortly after periastron passage; these appear to be caused by the passage of the orbit through the strong-field region close to the background Kerr black hole.

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Computational Methods for the Self-Force in Black Hole Spacetimes

Cited by 4 publications

References 115 publications

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime

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