I understand that magnetic force is a relativistic effect of electric force. Is there a force which is the relativistic effect of gravitational force? If a stationary observer sees 2 electrically charged particles moving parallel to each other at the same very high speed relative to himself he will see a "magnetic force" between the 2 particles. But an observer moving along with the charges would only see an electrostatic force between the particles. The "magnetic force" is just a relativistic effect of electric force. So, what if the particles were uncharged? Shouldn't there be a similar "relativistic- gravitational" force (analogous to magnetism) seen by the stationary observer? The "relativistic-gravitational" force would be very small, because gravitational force is generally much smaller than electric force (and relativistic force is very small relative to static force except at very high speeds). However, the universe contains massive galaxies moving at high speeds relative to one another. At that scale, the relativistic force should be observable. I think it would be a repulsive force. On the other hand, maybe the relativistic increase in mass with velocity would provide just enough extra gravitational attraction to exactly counteract the repulsive relativistic force.