Given that a Red Lanterns's rage is centrally felt over loss, he likely feels rage specifically over the loss of his sector, or the billions of years of his life lost …
The Red Lantern Corps is one of the nine Lantern Corps that draw power from the Emotional Electromagnetic Spectrum.
The Red Lantern Corps was formed by Atrocitus because of the rage he felt over being imprisoned and because due justice was not brought to the Guardians of the Universe, whose Manhunters had slaughtered almost the entirety of his Space Sector. Their power rings channel the emotion "rage," and the Red Lanterns are chosen from the angriest sentients in the universe. The original was the Green Lantern Corps, and the Red Lanterns have been enemies to the super-hero Green Lantern.