论文标题
Bianchi I Universe中的轴向引力波
Axial Gravitational Waves in Bianchi I Universe
论文作者
论文摘要
在本文中，我们研究了使用regge-wheeler仪表的Bianchi I宇宙中轴向重力波的传播。在此规格中，在轴向波的情况下，只有两个非零组件的$ h_ {μν} $：$ h_0（t，r）$和$ h_1（t，r）$。在没有物质的情况下，对于未扰动和轴向扰动的度量，磁场方程既是得出的。通过假设扩展标量$θ$与剪切标量$σ$成比例（以便$ a = b^n $，$ a $，$ b $是指标系数，而$ n $是任意常数），而波动方程的扰动参数参数$ h_0（te derive $ h_0（t the te derive），这些场方程是同时求解的。我们使用了变量分离的方法来解决此参数，并随后确定了$ H_1（T，R）$。然后，我们讨论一些特殊情况以解释结果。我们发现，背景时空的各向异性是导致引力波通过该时空传播时的阻尼。扰动取决于角动量$ l $的值。物质存在的场方程表明，轴向扰动的时空仅在流体的方位角速度中导致扰动，这使物质场不受干扰。
In this paper, we have studied the propagation of axial gravitational waves in Bianchi I universe using the Regge-Wheeler gauge. In this gauge, there are only two non-zero components of $ h_{μν} $ in the case of axial waves: $h_0(t,r)$ and $h_1(t,r)$. The field equations in absence of matter have been derived both for the unperturbed as well as axially perturbed metric. These field equations are solved simultaneously by assuming the expansion scalar $Θ$ to be proportional to the shear scalar $σ$ (so that $a= b^n$, where $a$, $b$ are the metric coefficients and $n$ is an arbitrary constant), and the wave equation for the perturbation parameter $h_0(t,r)$ have been derived. We used the method of separation of variables to solve for this parameter, and have subsequently determined $h_1(t,r)$. We then discuss a few special cases in order to interpret the results. We find that the anisotropy of the background spacetime is responsible for the damping of the gravitational waves as they propagate through this spacetime. The perturbations depend on the values of the angular momentum $l$. The field equations in the presence of matter reveal that the axially perturbed spacetime leads to perturbations only in the azimuthal velocity of the fluid leaving the matter field undisturbed.
