Suppose there are two charged particles separated by some distance $d$ both with an equal positive charge of $q$. The particles also have equal masses of $m$. $m$ and $q$ are chosen so the electrostatic repulsive force between the particles exactly equals the gravitational attractive force between them and the particles are stationary. Now suppose the charges of the particles are increased by some small $\epsilon$ so the particles are repelled from each other with a very small force.
Suppose also that the particles are moving at a constant relativistic velocity $v$ at a right angle to their separation. In the stationary reference frame, the particles' masses will increase by some amount so that the gravitational force between them is larger than the electrostatic force and they accelerate towards each other. But in the reference frame of the particles, their masses do not increase and so they are accelerating away from each other. What is the resolution to this paradox?