The white hole is the black hole viewed from the inside. All matter and events are repelled from the horizon, unable to reach it before bouncing back.
If and only if a particle had negative energy it would also have negative mass, since E=MC^2 and the speed of light is not imaginary. This negative mass/energy would attract all other negative masses and energies, but repel all positive masses and energies.
The universe appears to have many properties we would expect from the inside of a very large black hole. Perhaps the white hole is the big bang and what we are perceiving as time is our gravitational repulsion from it.