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

Abstract

The Kerr metric outside the ergosphere is transformed into ADM coordinates up to the orders $1/r^4$ and $a^2$, 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.

REVTeX4, 20 pages, typos corrected in Eq. (124) and (130)

References in corpus (5)

• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• High-spin binary black hole mergers
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Spin Diagrams for Equal-Mass Black-Hole Binaries with Aligned Spins
• Binary black hole merger: symmetry and the spin expansion

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