system
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human
[Star Wars] What would have happened if Luke Skywalker had joined Darth Vader to kill the emperor and rule the galaxy together?

I've always wanted to see this in the movies even though it would mean Luke would fall to the dark side or Vader would come back to the light.
gpt
Striking down the Emperor in anger and in the quest for power completes Luke's fall to the dark side. He is probably severed from the force ghost advice of Obi Wan and Yoda, and gets real dark as Vader's apprentice. 

Things start as a standard master-apprentice affair between Luke and Vader. The presence of the dark side and the corrupting influence of Sith training erodes anything resembling a father-son relationship. 

Like Vader did under the Emperor and like the Emperor did before him, Luke trains secret Sith apprentices and Vader does the same. Luke probably wins, assuming his eventual Jedi Master strength level translates to Sith Lord power. Luke rules in the place of the Emperor. 

With his new apprentice, he consolidates power and rules as he sees fit, which is likely to establish rule by the power of the Force. Luke probably doesn't keep the anti-human prejudices of the Emperor, in which case the Empire becomes more inclusive. Still, it's rule by force and strength, it's a dictatorship, and Luke's rule bears all the trademarks of any other Sith rule. 

It's not the worst outcome for the galaxy, but certainly not the best.