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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 $ell$-modes. We find that, despite first appearances, the Regge-Wheeler gauge metric perturbation is $C^0$ at the particle for all $ell$. As a first use of our solutions, we compute the gauge-invariant quantity $langle U rangle$ through 4PN while simultaneously expanding in eccentricity through $e^{10}$. By anticipating the $eto 1$ singular behavior at each PN order, we greatly improve the accuracy of our results for large $e$. We use $langle U rangle$ to find 4PN contributions to the effective one body potential $hat Q$ through $e^{10}$ and at linear order in the mass-ratio.
Using the post-Newtonian (PN) expansion technique of the gravitational wave perturbation around a Schwarzschild black hole, we calculate analytically the energy flux of gravitational waves induced by a particle in circular orbits up to the 5.5PN orde
[abridged] The inspiral of a stellar compact object into a massive black hole is one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna. We expect to be able to detect and analyze many cycles of t
We provide expansions of the Detweiler-Whiting singular field for motion along arbitrary, planar accelerated trajectories in Schwarzschild spacetime. We transcribe these results into mode-sum regularization parameters, computing previously unknown te
Accurately modeling astrophysical extreme-mass-ratio-insprials requires calculating the gravitational self-force for orbits in Kerr spacetime. The necessary calculation techniques are typically very complex and, consequently, toy scalar-field models
We study geodesics in the Schwarzschild space-time affected by an uncertainty in the mass parameter described by a Gaussian distribution. This study could serve as a first attempt at investigating possible quantum effects of black hole space-times on