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 nonzero components of [Formula: see text] in the case of axial waves: [Formula: see text] and [Formula: see text]. 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 [Formula: see text] to be proportional to the shear scalar [Formula: see text] (so that [Formula: see text], where [Formula: see text], [Formula: see text] are the metric coefficients and [Formula: see text] is an arbitrary constant), and the wave equation for the perturbation parameter [Formula: see text] has been derived. We used the method of separation of variables to solve for this parameter, and have subsequently determined [Formula: see text]. We then discuss a few special cases 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 [Formula: see text]. 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.

中文翻译：

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Bianchi I 宇宙中的轴向引力波

在本文中，我们使用 Regge-Wheeler 规范研究了 Bianchi I 宇宙中轴向引力波的传播。在这个规范中，在轴向波的情况下，[公式：见文本]只有两个非零分量：[公式：见文本]和[公式：见文本]。对于未扰动的度量和轴向扰动的度量，已经导出了没有物质的场方程。这些场方程通过假设展开标量 [公式：参见文本] 与剪切标量 [公式：参见文本] 成比例同时求解（因此 [公式：参见文本]，其中 [公式：参见文本]，[公式:see text] 是度量系数，[Formula: see text] 是任意常数），并且已经导出了扰动参数 [Formula: see text] 的波动方程。我们使用变量分离的方法来求解这个参数，并随后确定了[公式：见正文]。然后我们讨论一些特殊情况来解释结果。我们发现，背景时空的各向异性是引力波在通过该时空传播时衰减的原因。扰动取决于角动量的值[公式：见正文]。存在物质时的场方程表明，轴向扰动的时空仅导致流体方位角速度的扰动，使物质场不受扰动。我们发现，背景时空的各向异性是引力波在通过该时空传播时衰减的原因。扰动取决于角动量的值[公式：见正文]。存在物质时的场方程表明，轴向扰动的时空仅导致流体方位角速度的扰动，使物质场不受扰动。我们发现，背景时空的各向异性是引力波在通过该时空传播时衰减的原因。扰动取决于角动量的值[公式：见正文]。存在物质时的场方程表明，轴向扰动的时空仅导致流体方位角速度的扰动，使物质场不受扰动。