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

TL;DR

This paper derives new higher-order spin interaction Hamiltonians for binary black holes using Poincaré invariance, advancing the understanding of their dynamics in the ADM formalism.

Contribution

It completes the set of $1/c^4$ spin-interaction Hamiltonians involving nonlinear spin terms for binary black holes.

Findings

Derived new higher-order-in-spin Hamiltonians using Poincaré algebra.

Completed expressions for $S^3p$- and $S^2p^2$-Hamiltonians at linear order in G.

Found no quartic nonlinear $S^4$-Hamiltonians at linear order in G.

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 $G$.