Does the rotation of a massive body affect its $g$-field according to GR?

I want to know, according to GR, if a fast-rotating massive planet/star would affect its gravitational field. Especially, I want to know if, besides an ordinary $g$-field, there appears some kind of Coriolis effect. For a better perception, consider the following example:

A compartment is parted from a massive plant by a column all at rest WRT each other. Suppose that that end of the column located on the planet is frictionless so that as the planet rotates about its center, the column, as well as the compartment, does not rotate. (One end of the column slides onto the surface of the planet as the planet rotates, that is.) We know that if the planet does not rotate about its center, there is an ordinary $g$-field inside the compartment defined by the Schwarzschild metric. However, what if the planet rotates very fast, say, close to light speed? Is there something like the Coriolis force detected by the observer inside the compartment?