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.
我们在一个对希尔伯特-爱因斯坦-拉格朗日理论进行非局部曲率修正的理论中推导引力波。除了标准的两个无质量张量模,具有正极化和交叉极化、螺旋度2和角频率ω1,我们还获得了一个具有螺旋度0和角频率ω2的标量质量模,其极化是横向的。这是一种呼吸模式,在一个有效参数γ的最低阶,呈现出接近零平面波和零平面波之间的速度差。最后,根据Petrov分类,非局部重力的准Lorentz E(2)-不变类为N3型。这意味着引力波模式的存在(或不存在)与观察者无关。