标题： 高阶非局部引力中的引力辐射 显示英文标题

标题： Gravitational radiation in higher order non-local gravity

摘要： 在本文中，我们研究由非局部引力拉格朗日密度$\mathcal{L}_{g}=R+\sum_{h=1}^{n}a_{h}R\Box^{-h}R$描述的高阶非局部引力中的引力辐射。这种非局部引力理论在$k_{1}^{2}=0$下总是表现出张量横向引力辐射，对应角频率$\omega_{1}$，由两种标准的$(+)$和$(\times)$极化模式组成，无质量且自旋为 2。此外，在适当的约束和$n\geq 2$下，它还会表现出一种额外的横向标量引力辐射，自旋为 0。 它由与$n-1$个角频率$\omega_{2},\ldots,\omega_{n}$相关的$n-1$模式组成，每个模式在$\gamma$的最低阶近似下具有呼吸极化$(b)$，这是一个考虑了稍有质量的波和无质量波速度差异的参数。 借助 NP 形式主义，我们发现$E(2)$类非局部引力波在 Petrov 分类中为$N_{3}$，其中所有模式的存在与否都是观察者无关的。 此外，当满足某些条件时，标量辐射在$n=1$和$n=2$情况下是被禁止的。最后，在$\Box^{-1}$引力中，当$n=1$时，会在特定约束下出现一个可能的退化情况，其中存在连续无限多个横向的有质量标量呼吸模式，这在二维时空中的表现重现了 Polyakov 有效作用量。 显示英文摘要

摘要： In this paper we examine gravitational radiation in higher order non-local gravity described by the non-local gravitational Lagrangian density $\mathcal{L}_{g}=R+\sum_{h=1}^{n}a_{h}R\Box^{-h}R$. This non-local theory of gravitation always exhibits the tensor transverse gravitational radiation for $k_{1}^{2}=0$, corresponding to the angular frequency $\omega_{1}$, composed of two standard $(+)$ and $(\times)$ polarization modes, massless and of helicity 2. Furthermore, it shows, under suitable constraint and $n\geq 2$, an additional massive transverse scalar gravitational radiation with helicity 0. It is composed of $n-1$ modes associated to $n-1$ angular frequencies $\omega_{2},\ldots,\omega_{n}$, each of which of breathing polarization $(b)$ to lowest order in $\gamma$, a parameter that takes into account the difference in speed between the slightly massive wave and the massless one. Thanks to NP formalism, we find that the $E(2)$ class of non-local gravitational waves is $N_{3}$, according Petrov classification, where the presence or absence of all modes are observer independent. Also, the scalar radiation is forbidden for $n=1$ and $n=2$ cases, when some conditions are satisfied. Finally, in $\Box^{-1}$ gravity where $n=1$, a possible degenerate case with a continuous infinity of transverse massive scalar breathing modes appears under a particular constraint, which reproduces in two-dimensional spacetime the Polyakov effective action.