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  • High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary
Title: High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary
We derive new terms in the post-Newtonian (PN) expansion of the generalized redshift invariant hu tiτ 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 e16 through 6PN relative order, and separately to e10 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.  more » « less
Award ID(s):
2110335 1806447
PAR ID:
10544973
Author(s) / Creator(s):
Publisher / Repository:
Physical Review D
Date Published:
Journal Name:
Physical Review D
Volume:
108
Issue:
8
ISSN:
2470-0010
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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