This is a really interesting pairing to dissect because their canon dynamic in 'Homestuck' is so ambiguous, yet it leaves these massive, gaping holes that fanfiction just loves to fill. The central trope is definitely friends-to-lovers, but not the warm, fluffy kind. It's more like 'we've been through literal hell and back together, so our bond is forged in trauma.' That shared experience from the game creates a bedrock of mutual understanding that most other characters can't touch.
A lot of writers latch onto the 'mutual pining' angle, where they're both deeply aware of each other but trapped by their own issues. Sollux has his fatalism and split psyche, Aradia has her detachment and post-death perspective. The push-and-pull isn't about petty misunderstandings, but about fundamentally different ways of existing—one clinging to a doomed timeline, the other having transcended it. The angst potential is off the charts.
I've seen some fantastic fics that flip it, though. Instead of angst, they explore a weird, serene domesticity. Two characters who've seen the end of the world trying to build a quiet life together, where Aradia's calm acceptance grounds Sollux's anxiety. The trope there is 'finding peace in the aftermath,' which is surprisingly wholesome given the source material. It's less about grand romance and more about two broken pieces fitting together because their jagged edges match.
Ultimately, I think the defining trope is 'cosmically significant relationship.' Their connection is tied to timelines, death, and fate in a way that feels bigger than just two trolls. That scope lets fanfiction go in wildly different directions, from tragic epic to quiet slice-of-life, while still feeling true to the characters. My favorite interpretation is when Aradia's newfound vitality post-retrieval acts as a counterbalance to Sollux's gloom, a dynamic where her curiosity pulls him out of his shell.