Maybe a bit board question but:
Fixing a regular cardinal $\kappa$ in the ground model, I am looking for examples of set forcing notions which preserve regularity of $\kappa$ and add no new $\kappa$ - Aronjain tree definable in $\langle H_{\kappa}, \in\rangle$ in $V[G]$. However they may add "non-definable" $\kappa$ - Aronjain trees depending on the properties of the ground model.
Please introduce references. Other examples about Suslin and Kurepa trees are also welcome however Aronjain trees are of much interest to me.