Adiabatic evolution due to the conservative scalar self-force during orbital resonances

Abstract

We calculate the scalar self-force experienced by a scalar point-charge orbiting a Kerr black hole along $r\theta$-resonant geodesics. We use the self-force to calculate the averaged rate of change of the charge's orbital energy $⟨\dot{E}⟩$, angular momentum $⟨{\dot{L}}_z⟩$, and Carter constant $⟨\dot{Q}⟩$, which together capture the leading-order adiabatic, secular evolution of the point-charge. Away from resonances, only the dissipative (time anti-symmetric) components of the self-force contribute to $⟨\dot{E}⟩$, $⟨{\dot{L}}_z⟩$, and $⟨\dot{Q}⟩$. We demonstrate, using a new numerical code, that during $r\theta$ resonances conservative (time symmetric) scalar perturbations also contribute to $⟨\dot{Q}⟩$ and, thus, help drive the adiabatic evolution of the orbit. Furthermore, we observe that the relative impact of these conservative contributions to $⟨\dot{Q}⟩$ is particularly strong for eccentric 2:3 resonances. These results provide the first conclusive numerical evidence that conservative scalar perturbations of Kerr spacetime are non-integrable during $r\theta$ resonances.

30 pages, 6 figures, 3 tables; Updated to reflect published version

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