Gravitational radiation reaction to a particle motion
Gravitational radiation reaction to a particle motion
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DOI：
10.1103/physrevd.55.3457
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发表时间：
1996-06
影响因子：
5
通讯作者：
Y. Mino;M. Sasaki;Takahiro Tanaka
中科院分区：
文献类型：
--
作者：
Y. Mino;M. Sasaki;Takahiro Tanaka
已知在弯曲时空中运动的小质量粒子以相对于粒子质量的最低阶近似跟踪背景测地线。在本文中，我们讨论了粒子运动方程的前级修正，它可能描述了引力辐射反应的影响。我们用两种不同的方法推导出运动方程。第一个是DeWitt和Brehme为推导带电粒子的运动方程而发展的著名形式主义的扩展。构造守恒的二阶对称张量，并在环绕轨道的世界管内部积分它，我们得到了运动方程。虽然这种方法的计算很简单，但它包含了不那么严格的点。与电磁情况不同，电磁情况有两种不同的电荷，即电荷和质量，而引力对应的情况只有一种电荷。这一事实阻止了我们使用在电磁情况下使用的相同的重整化方案。为了克服这一困难，我们在计算定义小粒子动量的三个空间体积上的守恒张量的积分时使用了一个ansatz。为了阐明第一种方法的微妙之处，我们接着考虑了两种不同方案的渐近匹配，即内部方案和外部方案，在内部方案中，小粒子被表示为带有潮汐扰动的球对称黑洞，而外部方案中，度规是由给定背景几何上的小扰动来给出的。由匹配的一致性条件得到运动方程。我们发现，在这两种方法中，都得到了相同的运动方程。由此得到的运动方程与在电磁情况下得到的运动方程相似。我们讨论了这个运动方程的含义。PAC编号(S)：04.30。db，04.25。-g
A small mass particle traveling in a curved spacetime is known to trace a background geodesic in the lowest order approximation with respect to the particle mass. In this paper, we discuss the leading order correction to the equation of motion of the particle, which presumably describes the effect of gravitational radiation reaction. We derive the equation of motion in two different ways. The first one is an extension of the well-known formalism by DeWitt and Brehme developed for deriving the equation of motion of an electrically charged particle. Constructing the conserved rank two symmetric tensor, and integrating it over the interior of the world tube surrounding the orbit, we derive the equation of motion. Although the calculation in this approach is straightforward, it contains less rigorous points. In contrast to the electromagnetic case, in which there are two different charges, i.e., the electric charge and the mass, the gravitational counterpart has only one charge. This fact prevents us from using the same renormalization scheme that was used in the electromagnetic case. In order to overcome this difficulty, we put an ansatz in evaluating the integral ofthe conserved tensor on a three spatial volume which defines the momentum of the small particle. To make clear the subtlety in the first approach, we then consider the asymptotic matching of two different schemes, i.e., the internal scheme in which the small particle is represented by a spherically symmetric black hole with tidal perturbations and the external scheme in which the metric is given by small perturbations on the given background geometry. The equation of motion is obtained from the consistency condition of the matching. We find that in both ways the same equation of motion is obtained. The resulting equation of motion is analogous to that derived in the electromagnetic case. We discuss implications of this equation of motion. PACS number(s): 04.30.Db, 04.25.-g