I've been reading about Kenotic Christology this weekend, the view that in coming to earth, Jesus emptied Himself of certain attributes like omnipotence, omniscience- those things which are incompatible with human existence. Defining divinity proves to be a difficult task for kenoticism, because if Christ is really fully divine but at the same time has really emptied Himself of powers we usually associate with divine attributes, either we must concede that Christ is not fully divine, or we must modify those attributes which we call "divine."
I think the latter makes a lot of sense- for instance, to say that the divine attribute "omnipotence" must be understood as possibly self-limiting. If Jesus does not express His omnipotence while human, but lays it aside in an act of self-limitation, then perhaps preserving His divinity means tweaking the definition of being "all powerful" to something like this: God is all-powerful except when He limits His own power.
Obviously this has implications for what we have traditionally called the "immutability" of God; if God can put aside His omnipotence for a time and then re-assume it, doesn't this signal change within God? Aquinas, addressing God's changelessness, says, "Because God understands and loves Himself, in that respect they said that God moves Himself; not, however, as movement and change belong to a thing existing in potentiality, as we now speak of change and movement" (Prima Pars, Q. 9, Art. 1). So if God is moving Himself maybe this does not represent a true change in potential within God. I'm not so convinced this works, though, because in Jesus it still looks like His omnipotence is hovering in a potential rather than actual state. Which is okay, because kenoticists gladly grant the changeability in God.
Here's another interesting move prompted by Aquinas: if the divine essence is a relation between persons of the trinity, then Jesus' self limitation may be a temporary change of His attributes, but one which does not change the relation of Father to Son and Spirit to Son and Father to Spirit which is the divine essence. In Article 1, Question 39 of the Prima Pars, Aquinas discusses distinctions between persons of the Trinity but concedes that the divine essence is a relation:
"in creatures relations are accidental, whereas in God they are the divine essence itself. Thence it follows that in God essence is not really distinct from person, and yet that the persons are really distinguished from each other. For person signifies relation as subsisting in the divine nature."
So a distinction between the Father and the Son in terms of the actuality of their omnipotence would not be problem for divine attributes which kenoticism would have to solve; instead, the kenoticist could say that the attributes which Christ gives up in self-limitation do not rob Him of any divinity, because divinity is that relation between Christ and the other persons of the trinity which is not altered by His coming to earth as a man.
Enter Hans Urs von Balthasar: in his book on the descent of Christ into hell, he argues that on "Holy Saturday" Christ was really forsaken by the Father. Writing on von Balthasar, Edward T. Oakes argues that we cannot ignore "the transformation inside the Godhead itself that occurred when the Son of God descended as a dead man to be among the dead" (Oakes, "He descended into hell: The Depths of God's Self-Emptying Love on Holy Saturday in the Thought of Hans Urs von Balthasar" 238). If von Balthasar is right and Holy Saturday was a real event of "Godforsakenness" inside the Trinity, then we are still forced to concede the mutability of God even under Aquinas' conception of divine essence.