Journal
PHYSICAL REVIEW D
Volume 86, Issue 8, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.86.084059
Keywords
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Funding
- NSF [PHY 0503366, PHY 1001515]
- European Research Council [202996]
- Division Of Physics
- Direct For Mathematical & Physical Scien [1001515] Funding Source: National Science Foundation
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This is the first of two papers on computing the self-force in a radiation gauge for a particle of mass m moving in circular, equatorial orbit about a Kerr black hole. In the extreme-mass-ratio inspiral (EMRI) framework, with mode-sum renormalization, we compute the renormalized value of the quantity H : = 1/2 h(alpha beta)u(alpha)u(beta), gauge-invariant under gauge transformations generated by a helically symmetric gauge vector; here, h(alpha beta) is the metric perturbation, u(alpha) the particle's 4-velocity. We find the related order m correction to the particle's angular velocity at fixed renormalized redshift (and to its redshift at fixed angular velocity), each of which can be written in terms of H. The radiative part of the metric perturbation is constructed from a Hertz potential that is extracted from the Weyl scalar by an algebraic inversion T. S. Keidl et al., Phys. Rev. D 82, 124012 (2010). We then write the spin-weighted spheroidal harmonics as a sum over spin-weighted spherical harmonics Y-s(lm) and use mode-sum renormalization to find the renormalization coefficients by matching a series in L = l + 1/2 to the large-L behavior of the expression for H. The nonradiative parts of the perturbed metric associated with changes in mass and angular momentum are calculated in the Kerr gauge.
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