论文标题
高阶重力辐射非本地重力
Gravitational radiation in higher order non-local gravity
论文作者
论文摘要
在本文中，我们检查了由非本地重力拉格朗日密度$ \ MATHCAL {l} _ {g} = r+sum_ {h = 1}^{n} a_ {h} a {这种非本地引力理论总是表现出张张量的横向重力辐射，$ k_ {1}^{2} = 0 $，对应于角度频率$ $ω__{1} $，由两个标准$（+（\）$和$（\ times）$（\ times）$（\ times）$ polarlizative modes $ selicq and of helicq and of plusect and purthermore and purthermore，它，它，它，它，它，$ furthermore，它，它，它，它，它，它，它，$ furthermore，它，它，它，它，它，它是furthermore，它，它，它横向标量引力辐射带有螺旋度0。它由$ n-1 $模式组成，与$ n-1 $角度频率相关，$ω__{2}，\ ldots，ω__{n} $，每个呼吸极化$（b）$在$γ$中的最低量，一个少量差异，互为差异差不多，差异很小。多亏了NP形式主义，我们发现$ e（2）$类别的非本地引力波是$ n_ {3} $，根据Petrov分类，所有模式的存在或不存在都是独立观察者的。同样，当满足某些条件时，$ n = 1 $和$ n = 2 $的情况禁止标量辐射。最后，在$ \ box^{ - 1} $重力中，$ n = 1 $，可能会在特定的约束下出现具有连续无穷大的横向大规模标量呼吸模式的变性案例，该模式在特定的约束下出现，在二维时空中复制了Polyakov有效动作。
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 $ω_{1}$, 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 $ω_{2},\ldots,ω_{n}$, each of which of breathing polarization $(b)$ to lowest order in $γ$, 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.
