The normal Java rules apply - if you inject something which isn't serializable into a class declared serializable, you will get an error.
You should declare both of these transient.
That's ok for java.util.Logger. But Event is a Webbeans class, so why not making it serializable?
Why I don't experience the same strictness in Seam? I can inject an Events component into a session scoped one, without the need of the transient keyword.
Probably true :-)
File an issue in JIRA...