Gluck twists for higher genus surfaces

Question

I am familiar with the Gluck twist of a sphere in a 4-manifold and I am curious if there is a generalization to an arbitrary oriented surface in a 4-manifold. Namely, for $g > 0$ letting $\Sigma_g$ be the closed orientable surface of genus $g$, are there automorphisms of $\Sigma_g \times S^1$ that do not extend over $\Sigma_g \times D^2$?