General relativity at 0K Relativistic gravity affects particle in motion, does it affect particle that are resting too? How? and if not could one say that the matter at 0K is not affected by gravity?
I'm not a physicist; is just a thought and probably really naive.
 A: Yes, gravity affects particles at rest, and particles at rest affect gravity.
In GR, the  interaction between spacetime and matter and energy is described by Einstein's equation,

(from Wikipedia).
The term $T_{\mu\nu}$ on the right is the stress-energy tensor.  Matter at rest contributes to the $T_{00}$ term, even if the matter has no other interactions than gravitational, so matter at rest contributes to the curvature of spacetime.  If you have a lump of mass in space and you are not moving with respect to it, it will still attract you.
The motion of a particle acted on by gravity is described by a geodesic.  This is true whether or not the particle is at rest.  To test it, simply toss a ball up in the air.  It comes to rest at the top of its arc, but gravity still pulls on it and it still falls.
More importantly, the principle of relativity states that frames moving with respect to each other have the same physics.  (In GR, we are only going to compare such frames locally, but it doesn't impact the discussion much.)  So if a particle is stationary in one frame, it is moving in other frames which are equally good descriptions of the universe.  Thus, there is no such notion as "at rest", except relative to some particular frame with no special distinction.  Every particle is always at rest in some frame, so if gravity has no impact on particles at rest, it has no impact on anything!
