New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: redshift invariant

Abstract

The Detweiler-Barack-Sago redshift function for particles moving along slightly eccentric equatorial orbits around a Kerr black hole is currently known up to the second order in eccentricity, second order in spin parameter, and the 8.5 post-Newtonian order. We improve the analytical computation of such a gauge-invariant quantity by including terms up to the fourth order in eccentricity at the same post-Newtonian approximation level. We also check that our results agrees with the corresponding post-Newtonian expectation of the same quantity, calculated by using the currently known Hamiltonian for spinning binaries.

15 pages, revtex macros

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• Analytic post-Newtonian expansion of the energy and angular momentum radiated to infinity by eccentric-orbit non-spinning extreme-mass-ratio inspirals to 19PN
• Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting
• New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: gyroscope precession
• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary
• Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit
• Redshift factor and the small mass-ratio limit in binary black hole simulations