How does the Eddington limit make the gravitational field of stars asymmetric? This answer to Is the gravitational field of the sun uniform? says:

Very large stars are asymmetric due to being close to the Eddington limit. The Sun is too small of a star to have the kind of gravitational anomalies that very large stars and rocky planets exhibit.

which is really interesting but leaves me unsatisfied.
Question: How exactly does the Eddington limit make the gravitational field of stars asymmetric?


What does Eddington Limit (Eddington Luminosity) Show?

From wikipedia:

Eddington luminosity
Humphreys–Davidson limit
Hot, massive stars tend to be (a) asymmetric, due to their rapid rotation (at least on the main sequence); and (b) very luminous, and thus nearer to the Eddington limit, but the two aren’t causally connected to each other.  So perhaps that answer was using correlation in place of causation.
The rapid rotation is due to the fact that hot stars lack the dynamo-driven magnetic fields that let lower-mass stars shed angular momentum and spin down over time.  The high luminosity is just a natural consequence of maintaining the higher temperature and pressure needed to support the higher mass, i.e. to maintain hydrostatic equilibrium.
It is closer to being true the other way around: because of rapid rotation, the effective gravitational field at the star’s equator is lower, and thus that part of the star will be closer to the Eddington limit at a given luminosity than a non-rotating star would be.