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Effect of gravitational radiation reaction on nonequatorial orbits around a Kerr black hole

Fintan D. Ryan
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Abstract

The effect of gravitational radiation reaction on orbits around a spinning black hole is analyzed. Such orbits possess three constants of motion: $ι$, $e$, and $a$, which correspond, in the Newtonian limit of the orbit being an ellipse, to the inclination angle of the orbital plane to the hole's equatorial plane, the eccentricity, and the semi-major axis length, respectively. First, it is argued that circular orbits ($e=0$) remain circular under gravitational radiation reaction. Second, for elliptical orbits (removing the restriction of $e=0$), the evolution of $ι$, $e$, and $a$ is computed to leading order in $S$ (the magnitude of the spin angular momentum of the hole) and in $M/a$, where $M$ is the mass of the black hole. As $a$ decreases, $ι$ increases and $e$ decreases.

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Fintan D. Ryan. 1995-11-22. Effect of gravitational radiation reaction on nonequatorial orbits around a Kerr black hole. https://doi.org/10.1103/physrevd.53.3064

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