### Abstract

Recently, two independent calculations have been presented of finite-mass ("self-force") effects on the orbit of a point mass around a Schwarzschild black hole. While both computations are based on the standard mode-sum method, they differ in several technical aspects, which makes comparison between their results difficult-but also interesting. Barack and Sago invoke the notion of a self-accelerated motion in a background spacetime, and perform a direct calculation of the local self-force in the Lorenz gauge (using numerical evolution of the perturbation equations in the time domain); Detweiler describes the motion in terms a geodesic orbit of a (smooth) perturbed spacetime, and calculates the metric perturbation in the Regge-Wheeler gauge (using frequency-domain numerical analysis). Here we establish a formal correspondence between the two analyses, and demonstrate the consistency of their numerical results. Specifically, we compare the value of the conservative O(μ) shift in ut (where μ is the particle's mass and ut is the Schwarzschild t component of the particle's four-velocity), suitably mapped between the two orbital descriptions and adjusted for gauge. We find that the two analyses yield the same value for this shift within mere fractional differences of ∼10-5-10-7 (depending on the orbital radius)-comparable with the estimated numerical error.

Original language | English |
---|---|

Article number | 124024 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 78 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 2 2008 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*78*(12), [124024]. https://doi.org/10.1103/PhysRevD.78.124024

**Two approaches for the gravitational self-force in black hole spacetime : Comparison of numerical results.** / Sago, Norichika; Barack, Leor; Detweiler, Steven.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 78, no. 12, 124024. https://doi.org/10.1103/PhysRevD.78.124024

}

TY - JOUR

T1 - Two approaches for the gravitational self-force in black hole spacetime

T2 - Comparison of numerical results

AU - Sago, Norichika

AU - Barack, Leor

AU - Detweiler, Steven

PY - 2008/12/2

Y1 - 2008/12/2

N2 - Recently, two independent calculations have been presented of finite-mass ("self-force") effects on the orbit of a point mass around a Schwarzschild black hole. While both computations are based on the standard mode-sum method, they differ in several technical aspects, which makes comparison between their results difficult-but also interesting. Barack and Sago invoke the notion of a self-accelerated motion in a background spacetime, and perform a direct calculation of the local self-force in the Lorenz gauge (using numerical evolution of the perturbation equations in the time domain); Detweiler describes the motion in terms a geodesic orbit of a (smooth) perturbed spacetime, and calculates the metric perturbation in the Regge-Wheeler gauge (using frequency-domain numerical analysis). Here we establish a formal correspondence between the two analyses, and demonstrate the consistency of their numerical results. Specifically, we compare the value of the conservative O(μ) shift in ut (where μ is the particle's mass and ut is the Schwarzschild t component of the particle's four-velocity), suitably mapped between the two orbital descriptions and adjusted for gauge. We find that the two analyses yield the same value for this shift within mere fractional differences of ∼10-5-10-7 (depending on the orbital radius)-comparable with the estimated numerical error.

AB - Recently, two independent calculations have been presented of finite-mass ("self-force") effects on the orbit of a point mass around a Schwarzschild black hole. While both computations are based on the standard mode-sum method, they differ in several technical aspects, which makes comparison between their results difficult-but also interesting. Barack and Sago invoke the notion of a self-accelerated motion in a background spacetime, and perform a direct calculation of the local self-force in the Lorenz gauge (using numerical evolution of the perturbation equations in the time domain); Detweiler describes the motion in terms a geodesic orbit of a (smooth) perturbed spacetime, and calculates the metric perturbation in the Regge-Wheeler gauge (using frequency-domain numerical analysis). Here we establish a formal correspondence between the two analyses, and demonstrate the consistency of their numerical results. Specifically, we compare the value of the conservative O(μ) shift in ut (where μ is the particle's mass and ut is the Schwarzschild t component of the particle's four-velocity), suitably mapped between the two orbital descriptions and adjusted for gauge. We find that the two analyses yield the same value for this shift within mere fractional differences of ∼10-5-10-7 (depending on the orbital radius)-comparable with the estimated numerical error.

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U2 - 10.1103/PhysRevD.78.124024

DO - 10.1103/PhysRevD.78.124024

M3 - Article

AN - SCOPUS:58949103287

VL - 78

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 12

M1 - 124024

ER -