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The canonical Arnowitt-Deser-Misner (ADM) Hamiltonian with next-to-leadingorder spin-spin coupling [J. Steinhoff, S. Hergt, and G. Sch\"afer] isconverted into the EOB formalism of T. Damour, P. Jaranowski, and G. Sch\"aferfor the special case of spinning black hole binaries whose spins are alignedwith the angular momentum. In particular, we propose to include the new termsby adding a dynamical term of next-to-leading order to the Kerr parametersquared entering the effective metric. The modified EOB Hamiltonianconsistently reduces to the Kerr Hamiltonian as the mass ratio tends to zero;moreover, it predicts the existence of an Innermost Stable Circular Orbit. Wealso derive, for the general case of arbitrarily oriented spins but in thevanishing mass-ratio limit, a coordinate transformation that maps thenext-to-leading order spin-spin contribution of the ADM Hamiltonian to the EOBHamiltonian.Comment: 15 pages, 5 figures. Submitted to Phys. Rev.

Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling for two nonprecessing black holes with aligned spins