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

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