论后牛顿轨道和银河系中心恒星
On post-Newtonian orbits and the Galactic-center stars
摘要：
银河系中心附近的恒星在近心通过期间达到光速的几个百分点，这使得后牛顿效应可能被检测到。我们制定的轨道方程的哈密顿形式，使$O(v^2/c^2)$和$O(v^3/c^3)$后牛顿效应的克尔度规出现作为一个简单的推广开普勒问题。一个相关的微扰哈密顿量适用于光子路径。然后，我们推导出一个辛积分与自适应时间步长，快速和准确的数值计算后牛顿效应。使用这个积分器，我们探索相对论效应。以恒星S2为例，我们发现广义相对论在天体测量学中贡献了十分之一的质量，在运动学中贡献了数十个$\rm km s^{-1}$。(For最终与观测结果比较，来自引力场对光路的红移和时间延迟的贡献将需要计算，但我们在本文中尝试这些。）银河系中心区域的恒星、气体和暗物质的贡献在观测上仍然没有得到很好的约束，但是目前的模型表明，由此产生的牛顿轨道摄动可能与半长轴为$\gtrsim 0.01$ pc（或250 mas）的恒星的相对论效应具有相同的量级。尽管如此，相对论性扰动的已知和独特的{ \it时间依赖性}可能使从观测中解开和提取这两种效应成为可能。
英文摘要：
Stars near the Galactic center reach a few percent of light speed during pericenter passage, which makes post-Newtonian effects potentially detectable. We formulate the orbit equations in Hamiltonian form such that the $O(v^2/c^2)$ and $O(v^3/c^3)$ post-Newtonian effects of the Kerr metric appear as a simple generalization of the Kepler problem. A related perturbative Hamiltonian applies to photon paths. We then derive a symplectic integrator with adaptive time-steps, for fast and accurate numerical calculation of post-Newtonian effects. Using this integrator, we explore relativistic effects. Taking the star S2 as an example, we find that general relativity would contribute tenths of mas in astrometry and tens of $\rm km s^{-1}$ in kinematics. (For eventual comparison with observations, redshift and time-delay contributions from the gravitational field on light paths will need to be calculated, but we do attempt these in the present paper.) The contribution from stars, gas, and dark matter in the Galactic center region is still poorly constrained observationally, but current models suggest that the resulting Newtonian perturbation on the orbits could plausibly be of the same order as the relativistic effects for stars with semi-major axes $\gtrsim 0.01$ pc (or 250 mas). Nevertheless, the known and distinctive {\it time dependence} of the relativistic perturbations may make it possible to disentangle and extract both effects from observations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
