广义引力扩展理论中的后牛顿N体动力学
Post-Newtonian N-Body Dynamics in Extended Theories of Gravity
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中文总结 AI 辅助
本文推导了扩展引力理论中N体系统的1PN拉格朗日量及运动方程，揭示了三体效应和标量场的影响，并在广义相对论极限下恢复了经典方程。
中文摘要 AI 辅助
我们推导了标量-张量-四阶引力（STFOG）中相对论N体系统的完整第一后牛顿（1PN）拉格朗日量及其对应的运动方程，包括非交换谱几何（NCSG）领域作为特殊情况。在Φ~Ψ（γ~1）的 regime 中，通过标准后牛顿度规解线性化四阶场方程，并直接从点粒子作用构建变分拉格朗日量。所得到的动力学由三个约当函数ζ、W和Ξ支配，它们编码了标量、重力磁性和三体领域，并依赖于额外传播模式的有效质量（m_R，m_Y，m_φ）。在此背景下，我们表明在1PN级别，非线性度规分量^{(4)}g_{00}不起作用。上述扩展理论的1PN轨道运动因此以闭合形式获得，且在相应的广义相对论极限下恢复了爱因斯坦-infeld-hoffmann方程。该形式为太阳系、双星脉冲星如PSR J0737-3039、银河中心恒星轨道和三体系统等相对论天体力学提供了共同框架。
英文摘要
We derive the complete first post-Newtonian (1PN) Lagrangian and corresponding equations of motion for the relativistic $N$-body system in Scalar-Tensor-Fourth-Order Gravity (STFOG), including the Non-Commutative Spectral Geometry (NCSG) sector as a special case. In the regime $Φ\sim Ψ$ ($γ\sim 1$), the linearized fourth-order field equations are solved in the Standard Post-Newtonian gauge, and the variational Lagrangian is built directly from the point-particle action. The resulting dynamics is governed by three Yukawa functions $ζ$, $\mathcal{W}$ and $Ξ$, which encode the scalar, gravitomagnetic and three-body sectors and depend on the effective masses $(m_R,m_Y,m_ϕ)$ of the additional propagating modes. In this context, we show that the nonlinear metric component ${}^{(4)}\!g_{00}$ plays no role at 1PN level. The 1PN orbital motion of the above extended theories is thus obtained in closed form, and the Einstein--Infeld--Hoffmann equations are recovered in the corresponding general-relativistic limit. The formalism provides a common framework for relativistic celestial mechanics and applies to Solar System, binary pulsars such as PSR J0737-3039, Galactic-center stellar orbits and triple systems.
