Exact solutions of nonlocal gravity in a class of almost universal spacetimes

We study exact solutions of the infinite derivative gravity with null radiation which belong to the class of almost universal Weyl type III/N Kundt spacetimes. This class is defined by the property that all rank-2 tensors B-ab constructed from the Riemann tensor and its covariant derivatives have traceless part of type N of the form B(square)S-ab and the trace part constantly proportional to the metric. Here, B(square) is an analytic operator and S-ab is the traceless Ricci tensor. We show that the convoluted field equations reduce to a single nonlocal but linear equation, which contains only the Laplace operator Delta on 2-dimensional spaces of constant curvature. Such a nonlocal linear equation is always exactly solvable by eigenfunction expansion or using the heat kernel method for the nonlocal form factor exp(-l(2)Delta) (with l being the length scale of nonlocality) as we demonstrate on several examples. We find the nonlocal analogues of the Aichelburg- Sexl and the Hotta-Tanaka solutions, which describe gravitational waves generated by null sources propagating in Minkowski, de Sitter, and anti-de Sitter spacetimes. They reduce to the solutions of the local theory far from the sources or in the local limit, l -> 0. In the limit l ->infinity, they become conformally flat. We also discuss possible hints suggesting that the nonlocal solutions are regular at the locations of the sources in contrast to the local solutions; all curvature components in the natural null frame are finite and specifically the Weyl components vanish.