标题： 高阶远程引力中的引力波 显示英文标题

标题： Gravitational Waves in Higher Order Teleparallel Gravity

摘要： 高阶拉格朗日量（如$L_{\Box R}=-R+a_{0}R^{2}+a_{1}R\Box R$）的平行等价物可以通过边界项$B=2\nabla_{\mu}T^{\mu}$获得。 在此视角下，我们推导了存在物质时高阶平行引力场的场方程，特别是线性包含$\Box$算符的六阶理论。 在弱场近似下，推导出了这些理论的引力波解。 发现了三种极化状态：两个标准的$+$和$\times$极化，即2-螺旋无质量横向张量极化，以及一个0-螺旋有质量的部分横向和部分纵向标量极化。 此外，这些引力波表现出四种与四个自由度相关的振动模式：两个经典的频率为$\omega_{1}$的$+$和$\times$张量模式，与标准的具有$k^{2}_{1}=0$的爱因斯坦波有关；以及两个分别与频率$\omega_{2}$和$\omega_{3}$相关的混合纵向-横向标量模式，涉及两个不同的 4 波矢量$k^{2}_{2}=M_{2}^{2}$和$k^{2}_{3}=M^{2}_{3}$。 这四个自由度是个别模式的幅度，即 $\hat{\epsilon}^{(+)}\left(\omega_{1}\right)$， $\hat{\epsilon}^{(\times)}\left(\omega_{1}\right)$， $\hat{B}_{2}\left(\mathbf{k}\right)$和 $\hat{B}_{3}\left(\mathbf{k}\right)$。 显示英文摘要

摘要： The teleparallel equivalent of higher order Lagrangians like $L_{\Box R}=-R+a_{0}R^{2}+a_{1}R\Box R$ can be obtained by means of the boundary term $B=2\nabla_{\mu}T^{\mu}$. In this perspective, we derive the field equations in presence of matter for higher-order teleparallel gravity considering, in particular, sixth-order theories where the $\Box$ operator is linearly included. In the weak field approximation, gravitational wave solutions for these theories are derived. Three states of polarization are found: the two standard $+$ and $\times$ polarizations, namely 2-helicity massless transverse tensor polarizations, and a 0-helicity massive, with partly transverse and partly longitudinal scalar polarization. Moreover, these gravitational waves exhibit four oscillation modes related to four degrees of freedom: the two classical $+$ and $\times$ tensor modes of frequency $\omega_{1}$, related to the standard Einstein waves with $k^{2}_{1}=0$; two mixed longitudinal-transverse scalar modes for each frequencies $\omega_{2}$ and $\omega_{3}$, related to two different 4-wave vectors, $k^{2}_{2}=M_{2}^{2}$ and $k^{2}_{3}=M^{2}_{3}$. The four degrees of freedom are the amplitudes of each individual mode, i.e. $\hat{\epsilon}^{(+)}\left(\omega_{1}\right)$, $\hat{\epsilon}^{(\times)}\left(\omega_{1}\right)$, $\hat{B}_{2}\left(\mathbf{k}\right)$, and $\hat{B}_{3}\left(\mathbf{k}\right)$.