Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background

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Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background

Seth Hopper, Chris Kavanagh, Adrian C. Ottewill
Paper Phys. Rev. D 93, 044010 (2016) | 2016-04-02

Abstract

We present a method for solving the first-order field equations in a post-Newtonian (PN) expansion. Our calculations generalize work of Bini and Damour and subsequently Kavanagh et al., to consider eccentric orbits on a Schwarzschild background. We derive expressions for the retarded metric perturbation at the location of the particle for all ℓ-modes. We find that, despite first appearances, the Regge-Wheeler gauge metric perturbation is C0 at the particle for all ℓ. As a first use of our solutions, we compute the gauge-invariant quantity ⟨U⟩ through 4PN while simultaneously expanding in eccentricity through e^10. By anticipating the e→1 singular behavior at each PN order, we greatly improve the accuracy of our results for large e. We use ⟨U⟩ to find 4PN contributions to the effective one body potential Q through e^10 and at linear order in the mass-ratio.