The Eddington Luminosity (or Eddington Limit) is a maximum limit on the Luminosity of a star or other astronomical body. It is the point beyond which the gravitational force inward is overwhelmed by the outward force of the Radiation Pressure. If it were surpassed, the radiation pressure would push material out of the star, reducing its mass and thus bringing its luminosity down to the limit. It represents an upper bound on the luminosity of stars in Hydrostatic Equilibrium, though they generally are not close to it.
It is used to derive the characteristics of Black Holes from the luminosity of the resulting Quasars. The Eddington Accretion Rate is the Accretion Rate at which a black hole reaches Eddington luminosity.
The Eddington Limit is exceeded by supernovae, but not over a time-scale long enough to require hydrostatic equilibrium.