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- W4387503271 abstract "We derive new terms in the post-Newtonian (PN) expansion of the generalized redshift invariant $⟨{u}^{t}{⟩}_{ensuremath{tau}}$ for a small body in eccentric, equatorial orbit about a massive Kerr black hole. The series is computed analytically using the Teukolsky formalism for first-order black hole perturbation theory, along with the Chrzanowski, Cohen, Kegeles method for metric reconstruction using the Hertz potential in ingoing radiation gauge. Modal contributions with small values of $l$ are derived via the semianalytic solution of Mano-Suzuki-Takasugi, while the remaining values of $l$ to infinity are determined via direct expansion of the Teukolsky equation. Each PN order is calculated as a series in eccentricity $e$ but kept exact in the primary black hole's spin parameter $a$. In total, the PN terms are expanded to ${e}^{16}$ through 6PN relative order, and separately to ${e}^{10}$ through 8PN relative order. Upon grouping eccentricity coefficients by spin dependence, we find that many resulting component terms can be simplified to closed-form functions of eccentricity, in close analogy to corresponding terms derived previously in the Schwarzschild limit. We use numerical calculations to compare convergence of the full series to its Schwarzschild counterpart and discuss implications for gravitational wave analysis." @default.
- W4387503271 created "2023-10-11" @default.
- W4387503271 creator A5041772918 @default.
- W4387503271 date "2023-10-10" @default.
- W4387503271 modified "2023-10-12" @default.
- W4387503271 title "High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary" @default.
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- W4387503271 doi "https://doi.org/10.1103/physrevd.108.084012" @default.
- W4387503271 hasPublicationYear "2023" @default.
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