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Major spoilers for The Rise of Skywalker, Vader: Immortal, and Darth Vader: Dark Lord of the Sith.
Mustafar is one of the most recognizable Star Wars planets for its setting and huge importance to the story. From its first appearance in Revenge of the Sith, Mustafar has been notable for its volcanic form and the darkness surrounding it, but it wasn't always in such a state of decay. Revealed in the VR Vader: Immortal series, Mustafar was once a lush green landscape that was teeming with all sorts of life. The planet's transformation from this beautiful place to a place of darkness, then returning to its original state goes to echo the many themes of redemption shown throughout the Skywalker Saga.
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To understand the relationship between Mustafar and the redeemed Skywalkers, there needs to be an understanding of the planet's origins told from Vader: Immortal. When Mustafar was still a planet of wildlife, there lived the Corvax family. After a war came to Mustafar, Lord Corvax was killed in the ongoing battle and left Lady Corvax to mourn his death in great sorrow. In an attempt to bring back her husband, she tried using the power of the Bright Star artifact to try and revive him. Unfortunately, this action ended up destroying Mustafar and putting it into the fiery state that it's so iconic for.
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The main premise of Vader: Immortal brings us to the Imperial era, and like so many times before Lord Vader has decided to try and bring Padmé back to life. To do this he has forcibly sought the help of Lady Corvax's smuggler descendant to help him find the Bright Star and use it to bring back the love of his life. After conferring with the Mustafarians about their legacy, the smuggler finds out that Vader will destroy Mustafar and any planet he can to power this device for his selfish reasons. This leads to them destroying the Bright Star and restoring Mustafar to its prior state, leaving it to heal itself for however long that takes.
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If there is any person that the planet Mustafar can best be correlated with, it would be Darth Vader. It saw the fall of Anakin Skywalker and caused the life-changing injuries that placed him in his iconic suit. It is the very place that Vader brought his crystal to bleed it into his new Sith lightsaber, the place he later returned to so that he could make his evil castle and main base. It also is the location where Vader made his two attempts to bring back Padmé Amidala by opening a force portal in Darth Vader: Dark Lord of the Sith and transporting her back to the land of the living in Vader: Immortal.
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Anakin and Mustafar's relationship doesn't just end physically. Anakin was brought up to be the chosen one ever since he was first brought into the Jedi Order, a being set to bring balance to the force in the name of the light. As Anakin once was before his fall, Mustafar was also a place of brightness and life, even if that connection isn't related to the force in any way. Both ended up falling to darkness in the same manner, caused by someone trying to save the lives of those they loved. Anakin followed the dark side of the force so that he could save Padmé from her foreseen death while Mustafar's detriment was caused by Lady Corvax trying to bring her late husband back to life. The redemption of both also ended up happening due to the help of family ties, with Luke helping show Vader that he needed to come back to the light to defeat Palpatine and Lady Corvax setting up a system that allowed the player to restore Mustafar.
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Vader's deep darkness is mirrored by the darkness of Mustafar. His true evil stems from a place of selfishness, Vader wanting Padmé for himself without thinking of the millions he will kill in her revival and missing the fact that she is kept from him through hate of what he's become. This is shown not only when she disappears in Vader: Immortal when she sees Vader brutally killing the player but also in Darth Vader: Dark Lord of the Sith when Padmé escapes Vader after he entered the gateway just to bring her back to life. Mustafar's evil comes from selfishness of almost the exact same kind with Lady Corvax dooming her entire planet just to unsuccessfully bring back her dead husband.
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Vader's actions in Vader: Immortal help to show the state of mind he's in during that space of time. By holding on to hope of getting back Padmé (the whole reason he turned to the dark side in the first place) and sticking to his destructive plan that will end up killing off any chance of Mustafar gaining it's mini redemption or continuing to exist any longer, Vader is griping further into the dark side with no sign of choosing to return to the light. This goes to show that the events of the Original Trilogy are the true beginnings of his redemptive path, that until then he is still denying himself of his true destiny, that he must wait for the help of others before straying from this path.
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This connection between redemption and Mustafar does not just stop with Anakin but also carries on with his grandson Ben. We don't see Mustafar much in The Rise of Skywalker, but for the minute we see it it's focused completely on Kylo Ren. While his time on Mustafar is one when he's in the depths of evil, the rebirth of life around him due to the events of Vader: Immortal show that Kylo is on his path of redemption and that there is still light in him that will later restore him to Ben Solo by the end of the movie.
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While the symbolism with Kylo Ren ends there, Ben Solo's story mirrors the story of Vader: Immortal in a crucial way. At the climax of The Rise of Skywalker, Ben transfers his life energy to Rey so that he could revive her, killing himself in the process. This selfless act to save the woman he loves serves as a foil to how Lady Corvax selfishly chose to destroy her planet to save the man she loved. The fact that Ben succeeded where Corvax failed highlights the goodness inside Ben and shows the change in his character. Ben Solo's actions oppose those that created evil and instates him with the redemption he deserves.
The theme of redemption will always be one of the most prominent themes of the Skywalker Saga, and whether Mustafar's appearance through the two main examples of redemption was supposed to mean something or not it still tells greatly of the path to redemption. One can only hope if we ever see more of Mustafar's past as a lush world or if we'll be able to see it grow back into one in the distant future of Star Wars canon.