For mathematical convenience initial data sets in numerical relativity are often taken to be conformally flat. Employing the dual-foliation formalism, we investigate the physical consequences of this assumption. Working within a large class of asymptotically flat spacetimes we show that the ADM linear momentum is governed by the leading Lorentz part of a boost even in the presence of supertranslation-like terms. Following up, we find that in spacetimes that are asymptotically flat, and admit spatial slices with vanishing linear momentum that are sufficiently close to conformal flatness, any boosted slice can not be conformally flat. Consequently there are no conformally flat boosted slices of the Schwarzschild spacetime. This confirms the previously anticipated explanation for the presence of junk-radiation in Brandt-Bruegmann puncture data.

中文翻译：

---

渐近平坦时空的共形平坦切片

为了数学上的方便，数值相对论中的初始数据集通常被认为是共形平坦的。采用双叶形式主义，我们研究了这一假设的物理后果。在一大类渐近平坦的时空内工作，我们表明即使在存在超平移类项的情况下，ADM 线性动量也受升压的主要洛伦兹部分控制。接下来，我们发现在渐近平坦的时空中，并且允许线性动量消失且足够接近共形平坦度的空间切片，任何提升的切片都不能是共形平坦的。因此，没有施瓦西时空的共形平坦增强切片。这证实了先前预期的对 Brandt-Bruegmann 穿刺数据中存在垃圾辐射的解释。