Luke's hatred might be manifested in his actions during battles or confrontations. He may be more aggressive towards Vader in combat. Instead of trying to redeem Vader right away, in some fanfictions, he initially goes in with the sole intention of destroying Vader because of the pent - up hatred. He might use more force - based attacks and be less likely to show mercy, at least at the start of their encounters in the fan - created stories.
Often through his internal thoughts. The fanfiction might describe Luke seething with anger whenever he thinks of Vader. For example, in some stories, when Luke is meditating, his thoughts are constantly interrupted by visions of Vader and his past actions, and he can't focus because of his hatred.
His hatred can be shown in his interactions with others related to Vader. If he meets someone who was once associated with Vader, he might be cold or hostile. In a particular fanfiction, when Luke encounters a former Imperial officer who worked closely with Vader, he has a very difficult time restraining his anger and hatred towards that person just because of their connection to Vader.
It wasn't really shown directly in the movies. But we can assume that if he knew about it, he might have shown his dislike through his actions towards those who misrepresented the Jedi teachings which fanfiction might do.
Vader might initially be shocked. His son reaching out to him is unexpected. He could respond with a moment of silence, trying to process what is happening.
There's a fanfic titled 'Vader's Redemption'. In this story, Vader starts to question his loyalty to the Emperor much sooner, especially after some profound encounters with Luke. It's a great read as it shows the internal struggle of Vader while also exploring the bond between father and son in a new light. It's full of action-packed scenes and deep emotional moments.
This would be a huge twist. It might mean Luke is seduced by the dark side's power or has some ulterior motive for joining Vader. It could change the course of the entire story.
Luke as a spacer in fanfiction can also be a bit of a loner at times. He might prefer the solitude of space travel, using the time to meditate and strengthen his connection to the Force. But when he encounters trouble, he'll step up and use his Jedi skills to protect the innocent. One story could have him coming across a small, defenseless colony under attack by slavers. He would then use his lightsaber and the Force to drive off the slavers and free the colonists.
The relationship could develop in a complex way. Since Vader has captured Luke, there's a power imbalance. However, as they interact, Luke might try to reach out to the good in Vader. Vader, in turn, might be conflicted. He could start to protect Luke from the Emperor's harsher plans, leading to a strange alliance within the captivity.
One reason could be that Vader represents the dark side which has brought so much destruction in the galaxy. Luke, being on the side of the Jedi and good, would naturally despise the evil deeds associated with Vader.
In fanfiction, their relationship could develop more quickly towards mutual understanding. Maybe Luke could convince Vader to turn away from the dark side much earlier, and they could start training together as Jedi. This would be a huge shift from the original story.
In some fanfiction, if Luke and Darth Vader teamed up, they could be an unstoppable force for good. They could use their combined Force abilities to fight against a greater evil in the galaxy. Maybe they would start by taking on the Emperor together, using Vader's knowledge of the Sith and Luke's purity in the Force.
Their relationship could be shown as very conflicted. Darth Vader is deep in the Dark Side, but Ahsoka still remembers the good in Anakin. She might be angry at what he has become, while also feeling a sense of pity. Vader, on the other hand, might see her as a reminder of his failure as a Jedi.