Gödel's Universe and the Local Limit of Nonlocal Gravity

We consider the Gödel universe within the context of the local limit of nonlocal gravity. This theory differs from Einstein’s general relativity (GR) through the existence of a scalar susceptibility function $S(x)$ that is a characteristic feature of the gravitational field and vanishes in the GR limit. We show that Gödel’s spacetime is a solution of the modified gravitational field equations provided $S$ is a constant, in conformity with the spatial homogeneity of the Gödel universe.