AI 中文总结
本研究针对后闵可夫斯基三阶近似下的束缚态动力学，构建有效单天体理论的有效度规，通过两种对应策略验证径向作用量变量的一致性，采用类史瓦西各向同性规范确定3PM阶度规系数，为束缚态动力学提供一致有效度规。
AI 中文摘要
有效单天体（EOB）框架最初在后牛顿（PN）展开框架内构建，是引力波信号建模与解释的核心工具。近期研究已将后闵可夫斯基（PM）展开纳入EOB理论。本研究聚焦于PM近似下至三阶的束缚态动力学，构建EOB的核心要素——有效度规。我们检验了两种对应策略：一种基于径向作用量变量，另一种基于进动角。结果表明，径向作用量变量可提供一致的对应关系，这一点也通过基于进动角的对应关系得到验证。基于上述结果，我们采用类史瓦西参数化的各向同性规范来确定剩余自由度。在该参数化框架下，有效度规系数被确定至3PM阶。本研究结果为束缚态动力学提供了一致的有效度规。
英文摘要
The effective-one-body (EOB) framework, originally formulated within the post-Newtonian (PN) expansion, is central to modeling and interpreting gravitational-wave signals. Recent developments have incorporated the post-Minkowskian (PM) expansion into EOB theory. In this work, we focus on the bound state dynamics in the PM approximation up to the third order and construct the core ingredients of EOB: the effective metric. We examine two correspondence strategies, one based on the radial action variable and the other on the precession angle. We demonstrate that the radial action variable provides a consistent correspondence, which is further verified by the correspondence based on the precession angle. Building on these results, we adopt an isotropic gauge with a Schwarzschild-like parametrization to fix the remaining freedom. Within this parametrization, the effective metric coefficients are determined at 3PM order. Our results provide a consistent effective metric for the bound state dynamics.
Comments10 pages, one figure
