N体动力学中的后牛顿效应：相对论性进动和等级三元系中的守恒量
Post-Newtonian effects in N-body dynamics: Relativistic precession and conserved quantities in hierarchical triple systems
摘要：
传统的方法将广义相对论效应纳入到包含中心黑洞的N体系统的动力学中，或者包含相对论内双星的层次三元系统的动力学中，当目标是研究系统在与相对论长期效应相关的时间尺度上的演化时，例如近心点的岁差，可能是不够的。对于这样的问题，可能有必要在运动方程中加入后牛顿的“交叉项”，以便在长时间尺度上一致地捕捉相对论效应。交叉项是后牛顿（PN）项，它明确地将两体相对论扰动与系统中其他物体引起的牛顿扰动耦合起来。在本文中，我们证明了当且仅当运动方程中的PN交叉项效应被仔细地考虑时，一个分层三元系的总能量和总角动量的法向分量在内双星的相对论近心进动时标上明显地守恒到牛顿量级.
英文摘要：
Conventional approaches to incorporating general relativistic effects into the dynamics of N-body systems containing central black holes, or of hierarchical triple systems with a relativistic inner binary, may not be adequate when the goal is to study the evolution of the system over a timescale related to relativistic secular effects, such as the precession of the pericenter. For such problems, it may necessary to include post-Newtonian "cross terms" in the equations of motion in order to capture relativistic effects consistently over the long timescales. Cross terms are post-Newtonian (PN) terms that explicitly couple the two-body relativistic perturbations with the Newtonian perturbations due to other bodies in the system. In this paper, we show that the total energy and the normal component of total angular momentum of a hierarchical triple system is manifestly conserved to Newtonian order over the relativistic pericenter precession timescale of the inner binary if and only if PN cross-term effects in the equations of motion are taken carefully into account.
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