Although the Eddington limit has originally been derived for stars, recently its relevance for the evolution of accretion discs has been realized. We discuss the question whether the classical Eddington limit - which has been applied globally for almost all calculations on accretion discs - is a good approximation if applied locally in the disc. For this purpose, a critical accretion rate corresponding to this type of modified classical Eddington limit is calculated from thin alpha-disc models and slim disc models. We account for the non-spherical symmetry of the disc models by computing the local upper limits on the accretion rate from vertical and radial force equilibria separately. It is shown that the results can differ considerably from the classical (global) value: The vertical radiation force limits the maximum accretion rate in the inner disc region to much less than the classical Eddington value in thin alpha-discs, while it allows for significantly higher accretion rates in slim discs. We discuss the implications of these results for the evolution of accretion discs and their central objects.
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