标题： 通过准正则模和分支切割在施瓦茨希尔德时空中的自力和格林函数 显示英文标题

标题： Self-Force and Green Function in Schwarzschild spacetime via Quasinormal Modes and Branch Cut

摘要： 在弯曲背景时空中的一个小致密物体的运动由于其自身场的作用而偏离测地线，从而产生自力。 这种自力可以通过对小物体的过去世界线上的波方程的格林函数进行积分来计算。 我们使用匹配格林函数展开的半解析方法，以此方式计算史瓦西时空中的标量电荷的自力。 在致密物体的局部邻域内，该方法使用格林函数的Hadamard形式，以便使正则化变得简单。 在这个局部邻域之外，我们通过复频域中的极点（准正常模）和分支切割积分来进行格林函数的谱分解。 我们证明这两种展开在足够大的匹配区域内重叠，从而使自力的精确计算成为可能。 这里研究的标量情况是一个有用的且具有说明性的玩具模型，用于引力情况，它可用于模拟极端质量比极限下的天体物理双星系统。 显示英文摘要

摘要： The motion of a small compact object in a curved background spacetime deviates from a geodesic due to the action of its own field, giving rise to a self-force. This self-force may be calculated by integrating the Green function for the wave equation over the past worldline of the small object. We compute the self-force in this way for the case of a scalar charge in Schwarzschild spacetime, making use of the semi-analytic method of matched Green function expansions. Inside a local neighbourhood of the compact object, this method uses the Hadamard form for the Green function in order to render regularization trivial. Outside this local neighbourhood, we calculate the Green function using a spectral decomposition into poles (quasinormal modes) and a branch cut integral in the complex-frequency plane. We show that both expansions overlap in a sufficiently large matching region for an accurate calculation of the self-force to be possible. The scalar case studied here is a useful and illustrative toy-model for the gravitational case, which serves to model astrophysical binary systems in the extreme mass-ratio limit.