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There are extremely luminous quasi stellar objects (QSOs) at high redshiftwhich are absent at low redshift. The lower luminosities at low redshifts canbe understood as the external manifestation of either a lower Eddington ratioor a lower mass. To distinguish between both effects, we determine the possibledependence of masses and Eddington ratios of QSOs with a fixed luminosity as afunction of redshifts; this avoids the Malmquist bias or any other selectioneffect. For the masses and Eddington ratios derived for a sample of QSOs in theSloan Digital Sky Survey, we model their evolution by a double linear fitseparating the dependence on redshifts and luminosities. The validity of thefits and possible systematic effects were tested by the use of differentestimators of masses or bolometric luminosities, and possible intergalacticextinction effects. The results do not show any significant evolution of blackhole masses or Eddington ratios for equal luminosity QSOs. The black hole massonly depends on the bolometric luminosity without significant dependence on theredshift as M_{BH}(10^9 M_sun) = 3.4[L_{bol}(10^{47} erg/s})]^{0.65} on averagefor z<5. This must not be confused with the possible evolution in the formationof black holes in QSOs. The variations of environment might influence theformation of the black holes but not its subsequent accretion. It also leaves aquestion to be solved: Why are there not QSOs with very high mass at lowredshift? A brief discussion of the possible reasons for this is tentativelypointed out.

On the non-evolution of the dependence of black hole masses on bolometric luminosities for QSOs