The broader question is why any immortal entity would care about anything? Afterall, it is the alternative of life and death that gives rise to the concept of value. Quoting a famous passage from Ayn Rand's Virtue of Selfishness quoted here:
“Value” is that which one acts to gain and/or keep. The concept “value” is not a primary; it presupposes an answer to the question: of value to whom and for what? It presupposes an entity capable of acting to achieve a goal in the face of an alternative. Where no alternative exists, no goals and no values are possible.
I quote from Galt’s speech: “There is only one fundamental alternative in the universe: existence or nonexistence—and it pertains to a single class of entities: to living organisms. The existence of inanimate matter is unconditional, the existence of life is not: it depends on a specific course of action. Matter is indestructible, it changes its forms, but it cannot cease to exist. It is only a living organism that faces a constant alternative: the issue of life or death. Life is a process of self-sustaining and self-generated action. If an organism fails in that action, it dies; its chemical elements remain, but its life goes out of existence. It is only the concept of ‘Life’ that makes the concept of ‘Value’ possible. It is only to a living entity that things can be good or evil.”
To make this point fully clear, try to imagine an immortal, indestructible robot, an entity which moves and acts, but which cannot be affected by anything, which cannot be changed in any respect, which cannot be damaged, injured or destroyed. Such an entity would not be able to have any values; it would have nothing to gain or to lose; it could not regard anything as for or against it, as serving or threatening its welfare, as fulfilling or frustrating its interests. It could have no interests and no goals.