High post-Newtonian order gravitational self-force analytical results for eccentric orbits around a Kerr black hole

TL;DR

This paper provides the first analytical calculations of the redshift function for a small mass in eccentric orbit around a spinning black hole, incorporating eccentricity, spin effects, and high post-Newtonian order.

Contribution

It introduces the first analytic computation of the gauge-invariant redshift function for eccentric orbits around a Kerr black hole, including complex eccentricity and spin interactions.

Findings

Redshift contributions mixing eccentricity and spin effects

Results valid through second order in eccentricity and spin

Achieved eight-and-a-half post-Newtonian order accuracy

Abstract

We present the first analytic computation of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in {\it eccentric} orbit around a {\it spinning} black hole. Our results give the redshift contributions that mix eccentricity and spin effects, through second order in eccentricity, second order in spin parameter, and the eight-and-a-half post-Newtonian order.