Does nonlocal gravity yield divergent gravitational energy-momentum fluxes?

Energy-momentum conservation requires the associated gravitational fluxes on an asymptotically flat spacetime to scale as 1/r2, as r→, where r is the distance between the observer and the source of the gravitational waves. We expand the equations of motion for the Deser-Woodard nonlocal gravity model up to quadratic order in metric perturbations, to compute its gravitational energy-momentum flux due to an isolated system. The contributions from the nonlocal sector contains 1/r terms proportional to the acceleration of the Newtonian energy of the system, indicating such nonlocal gravity models may not yield well-defined energy fluxes at infinity. In the case of the Deser-Woodard model, this divergent flux can be avoided by requiring the first and second derivatives of the nonlocal distortion function f[X] at X=0 to be zero, i.e., f′[0]=0=f′′[0]. It would be interesting to investigate whether other classes of nonlocal models not involving such an arbitrary function can avoid divergent fluxes.