Weak 'Antigravity' Fields in General Relativity
  Within the weak-field approximation of general relativity, new exact solutions are derived for the gravitational field of a mass moving with arbitrary velocity and acceleration. A mass having a constant velocity greater than 3^-1/2 times the speed of light gravitationally repels other masses at rest within a narrow cone. At high Lorentz factors (gamma >> 1), the force of repulsion in the forward direction is about -8(gamma^5) times the Newtonian force, offering opportunities for laboratory tests of gravity at extreme velocities. One such experiment is outlined for the Large Hadron Collider. 
F. S. Felber