1305.5674 (Simone Balmelli et al.)

An Effective-One-Body Hamiltonian with next-to-leading order spin-spin
coupling for two nonprecessing black holes with aligned spins    [PDF]

Simone Balmelli, Philippe Jetzer

The canonical Arnowitt-Deser-Misner (ADM) Hamiltonian with next-to-leading order spin-spin coupling [J. Steinhoff, S. Hergt, and G. Sch\"afer, Phys. Rev. D 77, 081501 (2008)], [J. Steinhoff, S. Hergt, and G. Sch\"afer, Phys. Rev. D 78, 101503 (2008)] is converted into the EOB formalism of [T. Damour, P. Jaranowski, and G. Sch\"afer, Phys. Rev. D 78, 024009 (2008)] for the special case of spinning black hole binaries whose spins are aligned with the angular momentum. In particular, we propose to include the new terms by adding a dynamical term of next-to-leading order to the Kerr parameter squared entering the effective metric. The modified EOB Hamiltonian consistently reduces to the Kerr Hamiltonian as the mass ratio tends to zero; moreover, it predicts the existence of an Innermost Stable Circular Orbit. We also derive, for the general case of arbitrarily oriented spins but in the vanishing mass-ratio limit, a coordinate transformation that maps the next-to-leading order spin-spin contribution of the ADM Hamiltonian to the EOB Hamiltonian.

View original: http://arxiv.org/abs/1305.5674