Nonlocal modification of Newtonian gravity

The Newtonian regime of a recent nonlocal extension of general relativity is investigated. Nonlocality is introduced via a scalar “constitutive” kernel in a special case of the translational gauge theory of gravitation, namely, the teleparallel equivalent of general relativity. In this theory, the nonlocal aspect of gravity simulates dark matter. A nonlocal and nonlinear generalization of Poisson’s equation of Newtonian gravitation is presented. The implications of nonlocality for the gravitational physics in the solar system are briefly studied.

Figure 1

Phase portrait of system (b6), where $w$ is drawn versus $z$.