Page "Eddington luminosity" Paragraph 23

For accreting black holes, all the energy released by accretion does not have to appear as outgoing luminosity, since energy can be lost through the event horizon, down the hole.

Such sources effectively may not conserve energy.

Then the accretion efficiency, or the fraction of energy actually radiated of that theoretically available from the gravitational energy release of accreting material, enters in an essential way.