The mass-type quadrupole moment of inspiralling compact binaries (without spins) is computed at the fourth post-Newtonian (4PN) approximation of general relativity. The multipole moments are defined by matching between the field in the exterior zone of the matter system and the PN field in the near zone, following the multipolar-post-Minkowskian (MPM)-PN formalism. The matching implies a specific regularization for handling infra-red (IR) divergences of the multipole moments at infinity, based on the Hadamard finite part procedure. On the other hand, the calculation entails ultra-violet (UV) divergences due to the modelling of compact objects by delta-functions, that are treated with dimensional regularization (DR). In future work we intend to systematically study the IR divergences by means of dimensional regularization as well. Our result constitutes an important step in the goal of obtaining the gravitational wave templates of inspiralling compact binary systems with 4PN/4.5PN accuracy.

中文翻译：

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后牛顿四阶紧致二元系统的质量四极矩

在广义相对论的第四次后牛顿 (4PN) 逼近中计算了激励紧凑双星（无自旋）的质量型四极矩。多极矩是通过物质系统外部区域中的场与近区域中的 PN 场之间的匹配来定义的，遵循多极后闵可夫斯基 (MPM)-PN 形式主义。基于Hadamard有限部分过程，匹配意味着用于处理无穷远多极矩的红外(IR)发散的特定正则化。另一方面，由于通过 delta 函数对紧凑物体进行建模，计算需要紫外线 (UV) 发散，这些都是用维度正则化 (DR) 处理的。在未来的工作中，我们还打算通过维度正则化系统地研究 IR 分歧。