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No one has ever crossed the Sunset Sea to learn what lies on the other side.

Então falou Martin - Comércio com Asshai.

(Agosto de 26, 2000)

De wiki:

The Sunset Sea is the great, unexplored ocean lying to the west of Westeros. Numerous explorers have sailed into the Sunset Sea searching for new lands, but save a few small islands located several weeks' travel west of the Iron Islands, nothing has been found, or at least no explorers have returned home alive to talk about it.

Como os Sete Reinos parecem inspirados pelo GB, é possível que as terras a oeste dele sejam um pendente da América e ainda não foram descobertas.

O show e os livros estão em duas continuidades diferentes portanto, as respostas para ambos podem diferir.

Uma Canção de Gelo e Fogo

O responder por @Shevliaskovic faz uma boa citação do GRRM sobre o quão perigoso é atravessar o Mar do Sol, mesmo afirmando que ninguém jamais o atravessou com sucesso.

Is there any trade between Westeros and Asshai over the Sunset Sea, or are those uncharted waters?
Over the =Sunset= Sea? No. No one has ever crossed the Sunset Sea to learn what lies on the other side.
Trading ships bound for Asshai go east through the Summer Sea and the Jade Sea, which are connected by the straights at Qarth.
_{The Citadel, So Spake Martin}

Conhecemos um exemplo em que alguém tentou atravessar o mar do pôr do sol no passado; Brandon, o Shipwright, que tentou, mas nunca mais foi visto. Esse evento levou Brandon, o Burner, a incendiar os navios de seus pais e a pôr fim ao poder do norte no mar.

"Do you recall your history, Bran?" the maester said as they walked. "Tell Osha who they were and what they did, if you can."
He looked at the passing faces and the tales came back to him. The maester had told him the stories, and Old Nan had made them come alive. "...Theon Stark's the real thin one with the long hair and the skinny beard. They called him the 'Hungry Wolf,' because he was always at war. That's a Brandon, the tall one with the dreamy face, he was Brandon the Shipwright, because he loved the sea. His tomb is empty. He tried to sail west across the Sunset Sea and was never seen again. His son was Brandon the Burner, because he put the torch to all his father's ships in grief. There's Rodrik Stark, who won Bear Island in a wrestling match and gave it to the Mormonts. And that's Torrhen Stark, the King Who Knelt. He was the last King in the North and the first Lord of Winterfell, after he yielded to Aegon the Conqueror. ..."
_{A Game of Thrones, Bran VII}

Lorde Gylbert parece acreditar que existem terras além do Mar do Pôr-do-sol, embora este possa ser apenas um palpite, enraizado em histórias ou até mesmo vindo de um sonho.

Lord Gylbert began to speak.** He told of a wondrous land beyond the Sunset Sea**, a land without winter or want, where death had no dominion. "Make me your king, and I shall lead you there," he cried. "We will build ten thousand ships as Nymeria once did and take sail with all our people to the land beyond the sunset. There every man shall be a king and every wife a queen."
His eyes, Aeron saw, were now grey, now blue, as changeable as the seas. Mad eyes, he thought, fool's eyes. The vision he spoke of was doubtless a snare set by the Storm God to lure the ironborn to destruction.
_{A Feast for Crows, The Drowned Man}

Os nascidos de ferro parecem acreditar que há algo além do mar do pôr-do-sol, mas os meistres acreditam que isso é pura especulação.

Among the ironborn, it is said that the first of the First Men to come to the Iron Isles found the famous Seastone Chair on Old Wyk, but that the isles were uninhabited. If true, the nature and origins of the chair's makers are a mystery. Maester Kirth in his collection of ironborn legends, Songs the Drowned Men Sing, has suggested that the chair was left by visitors from across the Sunset Sea, but there is no evidence for this, only speculation.
_{The World of Ice and Fire, Ancient History: The Dawn Age}

No entanto, o Archmaster Haereg acreditava que a cadeira Seastone havia vindo do Sunset Sea antes de rejeitar a idéia como pura especulação.

Archmaester Haereg once advanced the interesting notion that the ancestors of the ironborn came from some unknown land west of the Sunset Sea, citing the legend of the Seastone Chair. The throne of the Greyjoys, carved into the shape of a kraken from an oily black stone, was said to have been found by the First Men when they first came to Old Wyk. Haereg argued that the chair was a product of the first inhabitants of the islands, and only the later histories of maesters and septons alike began to claim that they were in fact descended of the First Men. But this is the purest speculation and, in the end, Haereg himself dismissed the idea, and so must we.
_{The World of Ice and Fire, The Iron Islands}

Os próprios meistres até reconhecem que não sabem nada sobre o que existe além do mar do pôr-do-sol.

Sadly, the Citadel's knowledge grows thinner the farther we travel from the lands that the men of the east call the Sunset Kingdoms, for congress with the more distant realms of Essos has ever been sparse. We know even less about the southern reaches of Sothoryos and far Ulthos, and nothing at all about whatever lands may lie beyond the Last Light and across the Sunset Sea.
_{The World of Ice and Fire, Other Lands}

Os únicos mapas canônicos que temos são aqueles em As Terras de Gelo e Fogo e até onde sei, não incluem nada além do mar do pôr-do-sol.

Existem várias fontes que afirmam que as Ilhas de Ferro governam o mar do pôr-do-sol há séculos e o usam para viajar por certas partes de Westeros; incluindo Euron Greyjoy. No entanto, parece-me que essas fontes significam apenas as partes do mar que estão próximas a Westeros e não que elas tenham explorado profundamente nele.

Game of Thrones

Não consegui encontrar nenhuma informação no programa sobre o que é a oeste do mar do pôr do sol. No entanto, encontrei um artigo de Elio que discute a imagem em sua pergunta. Infelizmente, ele não detalha o que é a oeste.

Best of all, the article is heavily illustrated with concept art and high-resolution stills from the sequence. Plus, the highest resolution glimpse at the map that includes Essos ... including Essos’s eastern coast, on the opposite side of the Sunset Sea.
_{Game of Thrones, Art of the Title Interview}

Lady Crane e Arya conversam sobre isso e dizem que ninguém sabe.

ARYA: Essos is east and Westeros is west. But what’s west of Westeros?

LADY CRANE: I don’t know.

ARYA: Nobody does. That’s where all the maps stop.

LADY CRANE: The edge of the world, maybe.

ARYA: I’d like to see that.

_{Game of Thrones, Season 6 Episode 8, "No One"}

E mais tarde no episódio final, Arya sai para o oeste e menciona para os presentes que ninguém sabe o que está lá.

Jon: You think anyone will dare tell you women aren't allowed?

Arya: I'm not going back north.

Jon: Where are you going?

Arya: What's west of Westeros?

Jon:I don't know.

Arya: No one knows. It's where all the maps stop. That's where I'm going.

_{Game of Thrones, Season 8 Episode 6, "The Iron Throne"}

Além disso, não parece haver nada sobre o oeste no programa.

se você aumentar o zoom nos novos continentes, poderá ver pontos vermelhos, assim como os de westero que marcam as cidades no mapa, então também existem cidades.