Nonlinear gravitational self-force: second-order equation of motion
Nonlinear gravitational self-force: second-order equation of motion
复制标题
非线性重力自力：二阶运动方程
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Pound
中科院分区：
文献类型：
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作者：
A. Pound
当一个小的、不带电的、致密的物体浸入外部背景时空时，它的质量为零阶，在背景中作为测试粒子运动。在线性秩序下，它自己的引力场改变了它周围的几何形状，它作为一个测试粒子在满足线性化真空爱因斯坦方程的某个有效度量中运动。在信中[物理学]。[j]，使用一种匹配渐近展开的方法，我证明了同样的陈述在二阶下成立：如果物体的前阶自旋和四极矩消失，那么通过其质量的二阶，它在其局部邻域中定义的某个光滑的局部因果真空度量的测地线上运动。在这里，我将详细介绍该结果的推导过程。此外，我将先前在与洛伦兹光滑相关的量规中导出的结果推广到一类高度规则的量规，这些量规应该是数值自力计算的最佳选择。
When a small, uncharged, compact object is immersed in an external background spacetime, at zeroth order in its mass it moves as a test particle in the background. At linear order, its own gravitational field alters the geometry around it, and it moves instead as a test particle in a certain effective metric satisfying the linearized vacuum Einstein equation. In the letter [Phys. Rev. Lett. 109, 051101 (2012)], using a method of matched asymptotic expansions, I showed that the same statement holds true at second order: if the object's leading-order spin and quadrupole moment vanish, then through second order in its mass it moves on a geodesic of a certain smooth, locally causal vacuum metric defined in its local neighbourhood. Here I present the complete details of the derivation of that result. In addition, I extend the result, which had previously been derived in gauges smoothly related to Lorenz, to a class of highly regular gauges that should be optimal for numerical self-force computations.