Why wasn t Arwen allowed to go to the Undying Lands?
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.
After the death of King Elessar, Legolas made a ship in Ithilien, and through Anduin, he left Middle-earth to go over the sea. His strong friendship with Gimli prompted him to invite Gimli to go to the Undying Lands; making him the first and only Dwarf to do so.
The Undying Lands were a realm inhabited by Ainur and Eldar. The area included the continent of Aman and the island of Tol Eressëa. The ocean Belegaer separated the Undying Lands from the western shores of Middle-earth. Only immortals and ring-bearers were allowed to live in this realm.
The Valar do not have the power to take away the Gift of Men. Also, Sam eventually travels West as well. Gimli is allowed to go because of his unusual friendship with Legolas, and with Galadriel.
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.
However, Arwen begins to have a vision of foresight of a possible future. She watches a little boy running across the pathway and sees him being picked up by Aragorn while they are in Gondor. Arwen realizes that he is her son, Eldarion when she notices the star of Elendil on his necklace.
Gimli is 139 during the events of The Lord of the Rings. Dwarves have an average lifespan of 250 years; thus, being young and strong, he was selected by Elrond to represent the Dwarves as part of Frodo's company.
The actor is suffering from Legolas Syndrome — where you accidentally get cast into a role that suits you far more than your real-life looks, leaving you with a tricky predicament after the wrap party. Do you A) nick all the costumes and stay in character the rest of your working life, or B)
Legolas tells Gimli that his final count is 42 Uruks.
Generally, the Valar only permitted immortals the right to reside in the Undying Lands. In the Third Age, Frodo, Bilbo, and later Gimli got special dispensation to travel to the Undying Lands because they were ring-bearers. Going to Valinor did not grant them immortality.
Why did Gimli go to Undying Lands?
To put it plainly, The Shire had lost it's luster for him, and after finishing his book, he had little reason to stay. He also had been through enough trauma for several lifetimes and although he had been healed by Elrond he was in need of greater healing that he could only receive in Valinor.
So when she allows this incredible rarity to Gimli, she essentially gives him the three hairs that Feanor demanded of her, because she has looked into his soul and found that he has a good heart and that he desires them for nothing more than to treasure the beautiful days he spent in her lands.

Of course, there are potential explanations for why Gimli might have been unaware -- not the least of which is that a messenger dispatched to spread the news was killed by Orcs. In Peter Jackson's The Lord of the Rings, it's Gimli's ignorance of what happened in Moria that motivates him to visit Balin's kingdom.
Despite this, Gimli's personality traits from the books are still present, and his attempt to destroy the One Ring is a perfect example of this. The moment humorously showcases the ring's near-indestructibility while also being the only instance of a character being completely immune to its corruption.
It is to the Undying Lands that the White Ship sails at the end of The Lord of the Rings. The Ring-bearers, Bilbo Baggins and Frodo Baggins were among the very few mortal beings to set foot on the shores of the Undying Lands. Later Samwise Gamgee, and then Gimli and Legolas together, ventured for the Undying Lands.
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.
Why does Frodo leave Middle-earth? Frodo is tired. Frodo has been through the gauntlet and suffered tremendously. The elves offer him a reward for his bravery as ring bearer (a reward also given to Bilbo, and later to Samwise).
The elves, or the Eldar, are immortal in the sense that they cannot die from illness or old age, however they can be slain. If they do die, they are summoned to the Halls of Mandos on Valinor, where they may eventually be returned to a physical form, although only in Valinor.
Daughter of Elrond and granddaughter of Galadriel, Arwen was called the “Evenstar” and was accounted as the most beautiful of the final generation of elves.
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).
Is Arwen a powerful Elf?
Arwen is described as the “most beautiful of the last generation of High Elves in Middle-earth,” and can summon powerful water spirits. She goes out of her way to always help those in need as well.
After the death of Thorin in the Battle of Five Armies, Dain becomes King under the Mountain. He redeems the Arkenstone from Bard with a fourteenth of the treasure, which is used to re-establish Dale. Over the next three years, Bard rebuilds the city of Dale and becomes its ruler.
According to the movie people, Legolas is 2,931 years old - and according to the book people, Aragorn was born in the year 2931 of the Third Age, meaning that during the quest his birth year is the same number as Legolas's age.
In fact, there's only one line that Legolas says to Frodo: “And you have my bow.”
Tauriel truly threw a wrench in Legolas' life when he fell in love with her. She was brave, fierce, and a protective leader of the guard. He was meant to be the dutiful son of King Thranduil, but in loving her, he became a stubborn, masterful archer instead. He loved exploration and adventure over his duties.
Legolas's Family Tree
Yet, since Tolkien does give family trees for other important Elves in the book, such as Galadriel and Elrond, it's clear that Galadriel is not Legolas's mother. (Besides, she is one of the Noldor, not a Silvan or Sindar Elf.)
Legolas managed to kill a further six Uruk-hai before his luck ran out and he was overwhelmed. He finished by killing a total of 18, just two fewer than Gimli and therefore handing victory to the Dwarf – much to Sam's (and no doubt Adam's) delight! So, there you have it – conclusive proof* that Gimli is the mightier!
After the destruction of the Ring, Gimli leads many Dwarves south to Aglarond, becoming the first Lord of the Glittering Caves. They build "great works" in Rohan and Gondor, and replace the ruined gate of Minas Tirith with one made of mithril and steel.
Legolas : Final count, forty-two. Gimli : Forty-two? Oh, that's not bad for a pointy-eared elvish princeling.
Is Gimli the last Dwarf?
No, he is not. All the Dwarves who survived the battle against Smaug are still alive, and they rule a Dwarven Kingdom. At the time of the Council of Elrond, you can see Glóin at the counvil, and there were kings after him as well in Middle-Earth, so Gimli is hardly the last of his race.
They're not immortal. The Undying Lands do not confer immortality on mortals. This was the big lie that Sauron told to Ar-Pharazôn the Golden to persuade him to attack Valinor: that those who went there became immortal. In fact, being in Valinor itself actually shortens the lives of mortals.
Aman was known somewhat misleadingly as "the Undying Lands", but the land itself does not cause mortals to live forever. However, only immortal beings were generally allowed to reside there.
After the war
After Aragorn's death, Legolas made a ship in Ithilien and left Middle-earth to go over the sea. His strong friendship with Gimli prompted Legolas to invite him to accompany him to the Undying Lands; making him the first and only Dwarf to do so. He was never seen again in Middle-earth.
The Undying Lands are a place of extreme blessings, essentially the heaven counterpart of Middle Earth. Very few are permitted to go there after an ancient rift in which some elves chose immortality, and others chose to take on a mortal lifespan.
Gimli was descended from, but was not a member of the royal line. Through his father, Gimli was also the first cousin once removed of Balin, Lord of Moria, and his brother Dwalin, two more former companions of Bilbo.
The Ring cannot effect Tom Bombadil because he is outside the whole issue of Power and Domination; Tolkien uses Tom as an allegory that even this intense struggle between "good and evil" is only part of the whole picture of existence.
This is why Legolas is smiling in that scene when Gimli tells him what Galadriel's gift was. He's smiling because he knows the significance. He's smiling because he knows Galadriel looked at Gimli and decided he deserved more than the greatest Elf that ever lived, and twice that.
Historyedit. Before the Company of the Ring left Lothlórien, each of its members was presented with a gift by Galadriel. Boromir was given a belt of gold which he carried in the journey until the Breaking of the Fellowship.
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.
Would Gollum have been allowed to go to the Undying Lands?
Gollum would not pass through the Grey Havens to the islands because his mind is ruined and out of control. Unlike Frodo, his mind was adjusted to a correct level to understand.
If Aragorn were to live and Arwen remained an immortal elf, they would never ever ever see each other again. The only way for Arwen to stay with Aragorn, in life and in death, was to give up her immortality. (Even when elves die of unnatural means, they are still separated from the spirits of mortal men.)
Two years later, Gandalf departs Middle-earth for ever. He boards the Ringbearers' ship in the Grey Havens and sets sail to return across the sea to the Undying Lands; with him are his friends Frodo, Bilbo, Galadriel, and Elrond, and his horse Shadowfax.
Legolas never runs out of arrows, and his quiver just fills up at random. At other times, he has no arrows at all but goes through the motion of firing them. Presumably, this is a CGI error that failed to fill in the shot.
Elrond Half-elven is a fictional character in J. R. R. Tolkien's Middle-earth legendarium. Both of his parents, Eärendil and Elwing, were half-elven, having both Men and Elves as ancestors.
Frodo came of age as Bilbo left the Shire. Frodo inherited Bag End and Bilbo's ring. Gandalf, uncertain about the origin of the ring, warned Frodo to avoid using it and to keep it secret. Frodo kept it hidden for the next seventeen years, and it gave him the same longevity it had given Bilbo.
After his wife died in the year 61 of the Fourth Age (SR 1482), Sam entrusted the Red Book to his daughter, Elanor and left the Shire. Because he was also a Ring-bearer, he was allowed to pass over the Sea to be reunited with Frodo in the Undying Lands.
The Elves don't need to go to the Undying Lands. If they wish (which they seldom seem to do) they may stay in Middle-Earth until Dagor Dagorath [Doomsday]. On the other hand there isn't much left for an elf who stays behind. Your life would just be lurching in the shadows in an everchanging world.
Partially this was due to the unique situation of their ancestry: because of the complications of being descendants of marriages between mortals and immortals, Elrond and his brother Elros were given the choice of their own fates, to be mortal with humanity or immortal with the elves.
Aragorn, Arwen, and Elrond Are All Related
But yes, all three of them are members of the same family. The Cliff's Notes version of the story is this: Arwen is, of course, Elrond's daughter, but Aragorn's connection is more distant.
Does Frodo go to heaven?
Where did Frodo go at the end? Frodo goes to the Undying Lands with the elves. While the mortal human, hobbit, and dwarf characters discuss death and dying (and do plenty of it) in Lord of the Rings, the immortal elves don't talk about their end in the same manner at all.
Can you go back from Undying Lands? Once an Elf is granted passage from the Grey Havens to Valinor, they sail across the Sundering Seas and enter the Undying Lands, never to return to Middle-earth. Valinor is its own sort of heaven, an eternal land of paradise for Elves to live among the gods.