论文标题
分布应力 - 能量四极杆
The Distributional Stress-Energy Quadrupole
论文作者
论文摘要
我们调查了从世界线上的增量功能构建的压力能量张量。我们专注于四极杆，因为它们为重力波的主要来源创造了出色的模型，并且具有重要的新颖特征。与偶极子不同，我们表明四极杆具有20个自由组件，这些组件不是由应力 - 能量张量的特性确定的。这些需要源自基础模型，我们给出一个示例，从无分歧的灰尘中动机。我们表明，与四极杆的部分导数表示相对应的组件具有像自由一样的规格。我们给出涉及第二个衍生物和两个积分的坐标公式的更改。我们还展示了如何在不参考坐标系或度量的情况下定义四极杆。对于使用协变量衍生物的表示，我们展示了如何以坐标的方式将四极杆拆分为纯的单子，纯偶极子和纯四极杆。
We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on quadrupoles as they make an excellent model for the dominant source of gravitational waves and have significant novel features. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example motivated from a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the change of coordinate formula which involves second derivatives and two integrals. We also show how to define the quadrupole without reference to a coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a coordinate free way.
