We derive gravitational waves in a theory with non-local curvature corrections to the Hilbert–Einstein Lagrangian. In addition to the standard two massless tensor modes, with plus and cross polarizations, helicity 2 and angular frequency ω ₁, we obtain a further scalar massive mode with helicity 0 and angular frequency ω ₂, whose polarization is transverse. It is a breathing mode, which, at the lowest order of an effective parameter γ, presents a speed difference between nearly null and null plane waves. Finally, the quasi-Lorentz E(2)-invariant class for the non-local gravity is type N ₃, according to the Petrov classification. This means that the presence (or absence) of gravitational wave modes is observer-independent.

我们在对希尔伯特-爱因斯坦拉格朗日函数进行非局部曲率校正的理论中推导出引力波。除了标准的两个无质量张量模式（具有正极化和交叉极化、螺旋度 2 和角频率ω _{1 ）之外}，我们还获得了另一个具有螺旋度 0 和角频率ω _{2 的}标量质量模式，其极化是横向的。它是一种呼吸模式，在有效参数γ的最低阶，呈现几乎零和零平面波之间的速度差异。最后，非局部重力的准洛伦兹E (2)-不变类是类型N ₃，根据彼得罗夫分类。这意味着引力波模式的存在（或不存在）与观察者无关。