I think I realized what Aatrox's Celestial Concept is.

Appearntly, those who went through Ascension not only get some awesome power and change their bodies to something that resembles an animal, but also get connected and merged with an ideal or idea of something, much like the Aspects, like the Aspect of War or Protection. As the title says, I think I realized what Aatrox got in his kit. While I can't say the actual name of the concept, for not knowing the actual phenomenon (or its name in English because I'm not a native speaker of it), I can say it's got to do with the revival part of his old and new kit. The idea of pushing yourself so hard and believing in your cause and motive so hard, while utlizing your rage to literlly surpass death itself, something that's way harder and better then plain Dedication. How I realized:

1. Aatrox says that he loathes what he has become, a shadow of his old and glorious Ascended form, yet he keeps taunting and saying to people he's immortal. Kind of contradicting, unless you consider my theory, that his drive to break free from the curse of the sword, and by that kill the entire world including himself, is actually keeping him alive until he reaches that goal.
2. His "finest creation", according to his old version. Tryndamere can resist death itself through channeling his rage, losing himself in the heat of battle in order to reach his goal, AKA killing the enemy until he can face Aatrox, finally. Sounds familiar? It's Aatrox's ideal. WAAARGHbobo even says so in a response he made: " Literally the ideal/idea he represented ceased to exist when he was trapped. Human's no longer could even have the thought/idea he was the avatar of."- while the Idea itself and the act have been erased from the world, Aatrox is still the merged partner of it, therefore he can still control it, we even see it in Tryn's lore: "But the dark figure did not even lift his blade, and instead gave Tryndamere a knowing smile.."- a knowing smile of seeing another human, possibly a new vessel, using the actual idea he merged with. That's why no one knows how Tryndamere keeps this power, because the actual idea of it has been erased already. And that's why both Aatrox and Tryndamere share the power to surpass death itself without using some sort of known magic, like time or ressuraction/dark magic.