Spin-squared Hamiltonian of next-to-leading order gravitational interaction

Details Spin-squared Hamiltonian of next-to-leading order gravitational interaction Spin-squared Hamiltonian of next-to-leading order gravitational interaction

2008-09-12

arxiv.org/abs/0809.2200v3

Phys.Rev.D78:101503,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

REVTeX4, 10 pages, v2: minor improvements in the presentation, v3: added omission in Eq. (4) and corrected coefficients in the

Scientific paper

10.1103/PhysRevD.78.101503

The static, i.e., linear momentum independent, part of the next-to-leading order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the post-Newtonian (PN) approximation is calculated from a 3-dim. covariant ansatz for the Hamilton constraint. All coefficients in this ansatz can be uniquely fixed for black holes. The resulting Hamiltonian fits into the canonical formalism of Arnowitt, Deser, and Misner (ADM) and is given in their transverse-traceless (ADMTT) gauge. This completes the recent result for the momentum dependent part of the NLO spin(1)-spin(1) ADM Hamiltonian for binary black holes (BBH). Thus, all PN NLO effects up to quadratic order in spin for BBH are now given in Hamiltonian form in the ADMTT gauge. The equations of motion resulting from this Hamiltonian are an important step toward more accurate calculations of templates for gravitational waves.

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