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Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincar\'e invariance

Research paper by Steven Hergt, Gerhard Schäfer

Indexed on: 20 Nov '08Published on: 20 Nov '08Published in: General Relativity and Quantum Cosmology



Abstract

The fulfillment of the space-asymptotic Poincar\'e 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 $S^3p$- and the $S^2p^2$-Hamiltonians are completed. It is also shown that there are no quartic nonlinear $S^4$-Hamiltonians to linear order in $G$.