论文标题
二进制动力学通过$ \ mathcal {o}（g^2）$的旋转的第五强度
Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
论文作者
论文摘要
我们使用先前开发的基于散射散射的框架来确定具有任意旋转$ S $的通用二进制系统的两体汉密尔顿人。通过构建，这种形式主义绕过了具有非物理奇点或更高衍生物的困难。该框架先前已用于获得$ \ MATHCAL O（G^2）$二次旋转两体哈密顿量的确切速度依赖性。我们首先以$ g $为单位评估$ s^3 $散射角度和两体哈密顿量，其中不仅包括所有与通常的世界运营商相对应的操作员，而且还包括一个有趣的微妙之处。然后，我们在$ \ Mathcal O（G^2）$中评估$ s^4 $和$ s^5 $贡献，我们通过与Aligned-Spin结果进行比较来确认。我们猜想，一定的移位对称性以及对散射幅度的高能生长的限制指定了Kerr Black Hole的Wilson系数，以旋转中的所有订单，并确认它们通过$ S^4 $重现了先前验证的结果。
We use a previously developed scattering-amplitudes-based framework for determining two-body Hamiltonians for generic binary systems with arbitrary spin $S$. By construction this formalism bypasses difficulties with unphysical singularities or higher-time derivatives. This framework has been previously used to obtain the exact velocity dependence of the $\mathcal O(G^2)$ quadratic-in-spin two-body Hamiltonian. We first evaluate the $S^3$ scattering angle and two-body Hamiltonian at this order in $G$, including not only all operators corresponding to the usual worldline operators, but also an additional set due to an interesting subtlety. We then evaluate $S^4$ and $S^5$ contributions at $\mathcal O(G^2)$ which we confirm by comparing against aligned-spin results. We conjecture that a certain shift symmetry together with a constraint on the high-energy growth of the scattering amplitude specify the Wilson coefficients for the Kerr black hole to all orders in the spin and confirm that they reproduce the previously-obtained results through $S^4$.
