Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates

The Kerr metric outside the ergosphere is transformed into Arnowitt-Deser-Misner coordinates up to the orders 1/r⁴ and a², respectively, in radial coordinate r and reduced angular momentum variable a, starting from the Kerr solution in quasi-isotropic as well as harmonic coordinates. The distributional source terms for the approximate solution are calculated. To leading order in linear momenta, higher-order-in-spin interaction Hamiltonians for black hole binaries are derived.