自我力对中心客体的依赖
Dependence of Self-force on Central Object
摘要：
对于围绕静态球对称体的轨道上的粒子，我们研究了当中心体类型（即，Schwarzschild外部的内部度量的选择）被改变。虽然由于需要正则化而难以计算直的自作用力，但这种“自作用力差”可以直接从相关波动方程的模式函数计算。这种技术给出了一个简单的探针的（非）局部性的力，以及提供了一个简单的确定一个物体上的自作用力的实际好处，一个任意（静态球对称）中心体，一旦相应的结果为黑洞（或其他参考内部）是已知的。我们推导出一个一般表达式的自作用力差的情况下（可能非最小耦合）的标量电荷的模式和水平，并表示电磁和引力的情况下的推广。然后我们考虑轨道和/或中心体的具体选择。我们的主要发现是：（1）对于离中心体很远的静电荷，在最小耦合标量情形和电磁情形下，自作用力与中心体类型无关（但在非最小耦合标量情况下依赖）;（2）对于标量情形下薄壳时空的圆轨道，黑洞时空的自作用力的分数变化对于径向（保守）力比角（耗散）力;（3）（这些时空之间的）径向自作用力差对于静电荷和相同半径的圆形轨道非常一致。
英文摘要：
For a particle in orbit about a static spherically symmetric body, we study the change in self-force that results when the central body type (i.e., the choice of interior metric for the Schwarzschild exterior) is changed. While a straight self-force is difficult to compute because of the need for regularization, such a "self-force difference" may be computed directly from the mode functions of the relevant wave equations. This technique gives a simple probe of the (non)locality of the force, as well as offers the practical benefit of an easy determination of the self-force on a body orbiting an arbitrary (static spherically symmetric) central body, once the corresponding result for a black hole (or some other reference interior) is known. We derive a general expression for the self-force difference at the level of a mode-sum in the case of a (possibly non-minimally coupled) scalar charge and indicate the generalization to the electromagnetic and gravitational cases. We then consider specific choices of orbit and/or central body. Our main findings are: (1) For charges held static at a large distance from the central body, the self-force is independent of the central body type in the minimally coupled scalar case and the electromagnetic case (but dependent in the nonminimally coupled scalar case); (2) For circular orbits about a thin-shell spacetime in the scalar case, the fractional change in self-force from a black hole spacetime is much larger for the radial (conservative) force than for the angular (dissipative) force; and (3) the radial self-force difference (between these spacetimes) agrees closely for a static charge and a circular orbit of the same radius.
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