Construct exact nontrivial solutions of nonlocal gravity (NLG) beyond Minkowski spacetime

Construct exact, nontrivial spacetime solutions of the field equations of nonlocal gravity (NLG) beyond Minkowski spacetime, in either vacuum or with matter sources, within the full nonlinear nonlocal framework defined by the causal kernel K(x, x').

Background

The authors state that, in the nonlinear regime of NLG, exact nontrivial solutions have not been found; Minkowski spacetime remains the only known exact solution without gravity and sources, and de Sitter spacetime is not a solution. This highlights a fundamental gap in the theory: the absence of exact solutions with nontrivial curvature or matter content within the full nonlocal formulation.

While the present work demonstrates that Gödel’s universe can be obtained in the local limit of NLG with a constant susceptibility S, this result does not address the construction of exact solutions in the full nonlocal theory, leaving the broader problem unresolved.