不同规范下三阶半后牛顿阶的辐射反作用力驱动动力学
Radiation-reaction driven dynamics at the third-and-a-half post-Newtonian order in different gauges
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中文总结 AI 辅助
该研究针对一般轨道，在不同规范下推导三阶半后牛顿阶辐射反作用力驱动动力学，通过坐标变换简化了辐射反作用轨道修正解的求解过程。
中文摘要 AI 辅助
我们针对一般轨道，研究三阶半后牛顿阶辐射反作用力的坐标依赖定义。为（部分）确定其表达式，我们采用平衡法，该方法涉及系统损失的能量与角动量、肖特项，以及无穷远处的能量与角动量通量。当从一个坐标系转换到另一个坐标系时，仅后者是规范不变量。辐射反作用力与肖特项的规范依赖性由一组进入其定义的规范参数编码。我们展示如何在哈密顿框架中用相空间变量表示，将系统在调和坐标下的机械能与角动量损失，与另一坐标系中辐射反作用力的径向和方位分量关联起来。该方法的优势在于，仅需调和坐标与新坐标系下坐标和动量之间的坐标变换，无需再次求解平衡方程。我们针对阿诺维特-德塞-米斯纳（Arnowitt-Deser-Misner）坐标和有效一体（Effective-One-Body）坐标推导了该变换。在后一种情况下，我们还讨论了当前波形模型中采用的规范参数的一些简化选择。最后，我们展示如何通过变换文献中已知的调和坐标解，直接得到新坐标系下轨道的辐射反作用修正解，这是一个显著的简化，因为人们可以避免再次求解辐射反作用动力学。
英文摘要
We consider the coordinate-dependent definition of the radiation-reaction force at the third-and-a-half post-Newtonian order for general orbits. In order to (partially) determine its expression we refer to the balance method, involving the energy and angular momentum lost by the system, the Schott terms, and the energy and angular momentum fluxes at infinity. Only the latter are gauge-invariant quantities when passing from a coordinate system to another. The gauge dependence of both radiation-reaction force and Schott terms is encoded in a set of gauge parameters entering their definitions. We show how to relate the harmonic-coordinate losses of mechanical energy and angular momentum by the system with the radial and azimuthal components of the radiation-reaction force in a different coordinate system expressed in terms of phase-space variables in a Hamiltonian framework. The advantage of this approach is that only the coordinate transformation between harmonic coordinates and coordinates and momenta in the new coordinate system is needed, without solving again the balance equations. We derive such a transformation for both Arnowitt-Deser-Misner and Effective-One-Body coordinates. In the latter case we also discuss some simplifying choices of the gauge parameters adopted in current waveform models. Finally, we show how to obtain the solution for the radiation-reaction correction to the orbit in the new coordinate system simply by transforming the harmonic-coordinate solution known in the literature. This is a remarkable simplification, since one can avoid to solve again for the radiation-reacted dynamics.
