We compute the energy flux of the gravitational waves radiated by a particle of mass μ in circular orbits around a rotating black hole of mass M up to the 11th post-Newtonian order (11PN), i.e. v22 beyond the leading Newtonian approximationwhere v is the orbital velocity of the particle [L. Blanchet, Living Rev. Relativity 5, 3 (2002)]. By comparing the PN results for the energy flux with …