Pericenter advance in general relativity: comparison of approaches at high post-Newtonian orders
Pericenter advance in general relativity: comparison of approaches at high post-Newtonian orders
复制标题
广义相对论中的近心推进：后牛顿高阶方法的比较
DOI：
10.1088/1361-6382/ab1c53
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发表时间：
2018
影响因子：
3.5
通讯作者：
C. Will
中科院分区：
文献类型：
--
作者：
Alexandria Tucker;C. Will
在广义相对论中，一个测试物体围绕一个大质量物体的轨道的近心的推进可以用许多方法计算。在一种方法中，研究精确史瓦西几何中的测地线方程，并将近心点之间的角度作为轨道转折点之间的某个径向函数的积分。在另一种方法中，使用密切轨道要素描述轨道，并分析“拉格朗日行星方程”，该方程给出了在后牛顿（PN）修正对运动的扰动作用下要素的演化。在将扰动分离成周期性和长期性效应之后，得到了近心角长期变化率的方程。虽然不同的方法同意领先的后牛顿贡献的进步，他们不同意高阶PN修正。我们表明，这种分歧是虚幻的。当轨道变量在每种情况下表示的不变能量和角动量的轨道，并考虑到一个微妙的差异的意义上的“近心推进”之间的两种方法，我们显示的第三个后牛顿秩序，不同的方法实际上完全同意。
The advance of the pericenter of the orbit of a test body around a massive body in general relativity can be calculated in a number of ways. In one method, one studies the geodesic equation in the exact Schwarzschild geometry and finds the angle between pericenters as an integral of a certain radial function between turning points of the orbit. In another method, one describes the orbit using osculating orbit elements, and analyzes the ‘Lagrange planetary equations’ that give the evolution of the elements under the perturbing effects of post-Newtonian (PN) corrections to the motion. After separating the perturbations into periodic and secular effects, one obtains an equation for the secular rate of change of the pericenter angle. While the different methods agree on the leading post-Newtonian contribution to the advance, they do not agree on the higher-order PN corrections. We show that this disagreement is illusory. When the orbital variables in each case are expressed in terms of the invariant energy and angular momentum of the orbit and when account is taken of a subtle difference in the meaning of ‘pericenter advance’ between the two methods, we show to the third post-Newtonian order that the different methods actually agree perfectly.