Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance

Abstract

The fulfillment of the space-asymptotic Poincaré algebra is used to derive new higher-order-in-spin interaction Hamiltonians for binary black holes in the Arnowitt-Deser-Misner canonical formalism almost completing the set of the formally $1/c^4$ spin-interaction Hamiltonians involving nonlinear spin terms. To linear order in $G$, the expressions for the $S^{3}p$- and the $S^2{p}^2$-Hamiltonians are completed. It is also shown that there are no quartic nonlinear $S^4$-Hamiltonians to linear order in $G$.

REVTeX4, 14 pages; center-of-mass-vector corrected Eq. (2.25) and modified coefficients of the Hamiltonian Eq. (7.3) and corresponding source terms Eqs. (7.5) and (7.6) following hereof; version to appear in Phys Rev D

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