Accuracy of the post-Newtonian approximation. II. Optimal asymptotic expansion of the energy flux for quasicircular, extreme mass-ratio inspirals into a Kerr black hole

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We study the effect of black hole spin on the accuracy of the post-Newtonian approximation.

• We focus on the gravitational energy flux for the quasicircular, equatorial, extreme mass-ratio inspiral of a compact object into a Kerr black hole of mass M and spin J.
• For a given dimensionless spin a=J/M^2 (in geometrical units), the energy flux depends only on the orbital velocity v or (equivalently) on the Boyer-Lindquist orbital radius r.
• We investigate the formal region of validity of the Taylor post-Newtonian expansion of the energy flux (which is known up to order v^8 beyond the quadrupole formula), generalizing previous work by two of us.