标题： 粘性流体壳对引力波传播的影响 显示英文标题

标题： Effect of a viscous fluid shell on the propagation of gravitational waves

摘要： 在本文中，我们表明在某些情况下，通过粘性流体传播的引力波（GWs）的阻尼可能非常显著；特别是，这适用于核心坍缩超新星（CCSNe）。 在以前的工作中，我们在Bondi-Sachs形式下使用固定背景上的线性扰动，以确定尘埃壳对GW传播的影响。 在这里，我们从（先前找到的）物质的速度场出发，并用它来确定流体流动的剪切张量。 然后，对于粘性流体，计算出耗散的能量，从而得到一个关于GW阻尼的方程。 发现当波长$\lambda$远小于物质壳的半径$r_i$时，阻尼效应与之前的结果一致；但如果$\lambda\gg r_i$，则阻尼效应大大增加。 接下来，本文讨论了一个天体物理应用，即CCSNe。 有几种不同的物理过程会产生GWs，文献中已经提出了许多模型。 因此，需要针对参数$\lambda,r_i$和剪切粘度系数$\eta$的每一个进行评估，这些参数具有不同的取值范围。 发现大多数情况下都会有显著的阻尼，在某些情况下甚至几乎完全阻尼。 我们还考虑了粘性阻尼对早期宇宙暴胀期间产生的原初引力波（pGWs）的影响。 研究了两种情况，其中波长要么远小于壳层半径，要么远大于壳层半径；我们发现存在一些条件会导致显著的阻尼，以至于这些波将无法被探测到。 显示英文摘要

摘要： In this paper we show that there are circumstances in which the damping of gravitational waves (GWs) propagating through a viscous fluid can be highly significant; in particular, this applies to Core Collapse Supernovae (CCSNe). In previous work, we used linearized perturbations on a fixed background within the Bondi-Sachs formalism, to determine the effect of a dust shell on GW propagation. Here, we start with the (previously found) velocity field of the matter, and use it to determine the shear tensor of the fluid flow. Then, for a viscous fluid, the energy dissipated is calculated, leading to an equation for GW damping. It is found that the damping effect agrees with previous results when the wavelength $\lambda$ is much smaller than the radius $r_i$ of the matter shell; but if $\lambda\gg r_i$, then the damping effect is greatly increased. Next, the paper discusses an astrophysical application, CCSNe. There are several different physical processes that generate GWs, and many models have been presented in the literature. The damping effect thus needs to be evaluated with each of the parameters $\lambda,r_i$ and the coefficient of shear viscosity $\eta$, having a range of values. It is found that in most cases there will be significant damping, and in some cases that it is almost complete. We also consider the effect of viscous damping on primordial gravitational waves (pGWs) generated during inflation in the early Universe. Two cases are investigated where the wavelength is either much shorter than the shell radii or much longer; we find that there are conditions that will produce significant damping, to the extent that the waves would not be detectable.