Abstract

It is shown that negatively gravitating particles can consistently be considered to exist and interact with normal positively gravitating particles in the contexts of general relativity and classical Newtonian gravitational theory. This issue arises from the discovery of dark energy which is considered to be causing an acceleration of the expansion of the universe. The issue is, can this dark energy occur in particulate form? A related issue was studied in the fifties by Herman Bondi. He investigated the possible existence of negative mass in the general relativity context, long before dark energy appeared on the scene. He came to a paradoxical conclusion that seemed to rule out the actual physical existence of negatively gravitating particles. This paradox does not occur in this work because only positive mass particle are involved whatever their gravitational character may be. The structure of the differential equations that would apply in the case of a binary pair of opposite gravitational character components are used to show and explain how they can become consistent in general relativity or classical gravitation theory. This involves explaining a non-obvious relation between the principle of equivalence and Newton's ?Action Equals Reaction? principle. A path structure for a mixed mass binary pair is set up which satisfies the equations of motion and does not have paradoxical properties. The force structure of the system is checked with a known classical dynamical test for the force per unit mass involved in the component particles motions. This test is used to demonstrate that the basic assumptions of this theory are incorporated into the consequential orbital structure. An alternative to the ?Action Equals Reaction? principle more appropriate to the astronomical situation is suggested. An animation using Mathematica has been derived, and is available, and shows how a mixed gravity binary pair move under their mutual gravitational action.