Gravitational radiation in higher order non-local gravity

In this paper, we examine gravitational radiation in higher order non-local gravity described by the Lagrangian density [Formula: see text]. This theory of gravitation always exhibits tensor transverse for text], corresponding to angular frequency composed two standard text] and polarization modes, massless helicity 2. Furthermore, it shows, under suitable constraint an additional massive scalar with 0. It is modes associated frequencies each which breathing lowest a parameter that takes into account difference speed between slightly wave one. Thanks NP formalism, find class waves according Petrov classification, where presence or absence all are observer independent. Also, forbidden cases, when some conditions satisfied. Finally, possible degenerate case continuous infinity appears particular constraint, reproduces two-dimensional spacetime Polyakov–effective action.