标题： 由具有非线性耦合的点粒子产生的二阶标量扰动的正则化 显示英文标题

标题： Regularization of second-order scalar perturbation produced by a point-particle with a nonlinear coupling

摘要： 准确计算由超大质量黑洞引起的背景时空中的致密物体运动，对于未来通过引力波探测器LISA检测此类双星系统是必要的。 达到所需的精度需要计算由致密物体产生的二阶引力扰动。 在点粒子极限情况下，二阶引力扰动方程表现出高度奇异的源项，标准的迟滞解在此情况下发散。 在这里，我们研究了一个简化的标量玩具模型，在该模型中，点粒子在给定的弯曲时空中引起非线性标量场。 在这个模型中，相应的二阶标量扰动方程也具有类似的奇异源项，因此其标准的迟滞解发散。 我们开发了一种正则化方法，用于构建该方程的定义良好的因果解。 值得注意的是，这些解与标准的迟滞解不同，在这种情况下标准的迟滞解是未定义的。 显示英文摘要

摘要： Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired accuracy requires calculation of the second-order gravitational perturbations produced by the compact object. At the point particle limit the second-order gravitational perturbation equations turn out to have highly singular source terms, for which the standard retarded solutions diverge. Here we study a simplified scalar toy-model in which a point particle induces a nonlinear scalar field in a given curved spacetime. The corresponding second-order scalar perturbation equation in this model is found to have a similar singular source term, and therefore its standard retarded solutions diverge. We develop a regularization method for constructing well-defined causal solutions for this equation. Notably these solutions differ from the standard retarded solutions, which are ill-defined in this case.