The logic is that Arwen chose to be mortal but she was not tied to
Arwen isn't necessarily dying because of the Ring, but now that she is mortal, she is dying through the slow decaying of time. Arwen also faces the same fate as all those in Middle Earth should the Ring Bearer fail his mission. So in that way, her fate is tied to the Ring.
Lùthien chose to live out her days as a mortal woman because she was in love. Arwen made a similar choice. Basically, this is what Arwen and Lùthien did: They chose not to 'part' with their parents and go to the Undying Lands, instead marrying/falling in love with a mortal, sealing their fate and rendering them mortal.
And after their marriage, both Aragorn and Arwen are mortal. Arwen, therefore, could not set foot in the Undying Lands without special permission. And she wouldn't be likely to go after it in the end. So unfortunately, she would not go there, unlike Legolas, after Aragorn's passing.
At this point Arwen has already given up her immortality, but now she grants the grace of the Eldar to Frodo, not giving him immortality since he is not one of the elves, but instead granting him a home in the undying lands when he does pass.
However, he does not possess the ability to live forever, and he cannot choose to be mortal or immortal like Arwen, the half-Elf he loves and eventually claims as his wife. Because Aragorn is mortal and Arwen chose to remain in Gondor and become mortal, their son, Eldarion, is mortal as well, despite his Elven lineage.
Arwen reciprocated Aragorn's love, and on the mound of Cerin Amroth they committed themselves to marrying each other. In making that choice, Arwen gave up the Elvish immortality available to her as a daughter of Elrond, and agreed to remain in Middle-earth instead of travelling to the Undying Lands.
Arwen didn't want Aragorn to die, because if he died so would she. She said she wasn't tired of living yet. But instead, Aragorn chose to die and Arwen lived a year longer before dying herself.
Arwen was her granddaughter
Galadriel and Celeborn had a daughter named Celebrian, who married Elrond and became the mother of Arwen (as well as her brothers, Elladan and Elrohir).
Never. That was the point. She was smitten with him and he refused as he was pledged to another. Unlike many other medieval stories, he never cheated, and she had to finally realize that he was never going to give in and she had to find one who was her equal and willing in Faramir.
Her constitution already severely weakened by loneliness and despair, combined with physical injuries, Éowyn then succumbed to the Black Breath. Théoden, not knowing that she was nearby, told Merry with his dying words that she had been "dearer than daughter" to him.
Princess Arwen Evenstar gave her beautiful necklace to Aragon to pledge her eternal love to him. This special gift from an immortal elf to a mortal man symbolized Arwen's decision to forsake her immortality to be with the person she truly loves.
She has a vision of a child clothed in white running across her path. She watches as the boy runs with his arms outstretched to his father, an aged Aragorn, who picks him up with joy and kisses him. As the boy looks at her and she sees he is wearing the Evenstar, she knows the boy to be her child.
No, their children and other descendants will be mortal. Arwen gave up her immortality to marry Aragorn and thus could not pass it on.
In the year 121 of the Fourth Age, after Aragorn's death, Arwen died of a broken heart at Cerin Amroth in Lórien, and was buried there one year after the death of Aragorn, to whom she had been wedded for 122 years. She was 2901 years old.
Elves are immortal but can be killed in battle, in which case they go to the Halls of Mandos in Aman. They may be restored by the Will of the Valar, and then go to live with the Valar in Valinor, like an Earthly Paradise, though just being in the place does not confer immortality, as Men supposed.
Originally, Tolkien intended for Éowyn to marry Aragorn. Later, however, he decided against it because Aragorn was "too old and lordly and grim". He considered making Éowyn the twin sister of Éomund, and having her die "to avenge or save Théoden".
Sauron Feared Galadriel
Tolkien also stated that Sauron saw Galadriel as his equal, and therefore, in his rise to power he feared that she would go after that power herself. As we saw in The Fellowship of the Ring, Galadriel told Frodo that the One Ring would consume her and turn her into a Dark Queen.
They are both elvish nobles, as Legolas is the son of King Thranduil and Arwen is the daughter of Elrond. They are both well-educated and would have known each other as the community of elves is quite small. It's likely they would have been at least friendly with one another.
Legolas Was 2,931 Years Old (in the Films)
Tolkien actually never specified an age for the bow-toting Silvan Elf.
When they meet, Arwen is thousands of years old with immortal beauty and he a young 20-something man. However, next time they meet, Aragorn is in his 50s. This was when Arwen fell in love with him, so his 30 years of maturing must have done some good.
Aragorn led the forces of the Reunited Kingdom on military campaigns against some Easterlings and Haradrim, re-establishing rule over much territory that Gondor had lost in previous centuries. He died at the age of 210, after 122 years as king.
Eowyn was left to lead the nation in his stead, as she was brave and beloved by the people. She led the people of Edoras to the White Mountains, where they took shelter. She stayed with them (albeit reluctantly) while the men fought in the Battle of Helms Deep.
Because he was the King of Gondor, a Man and a mortal, and he had no reason to abandon his duty. And as a descendent of Elros, he wasn't offered a choice.
Eventually, Legolas came to Ithilien with some of his people, with his father's leave, to live out his remaining time in Middle-earth helping to restore the devastatedforests of that war-ravaged land.