Could you show a comparative analysis on Yeats's poem and Robert Silverberg's novella Sailing to Byzantium?

Silverberg's award-winning novella is based on Yeats's poem of the same name and quotes from it. Both works share similarities: each evokes mystically beautiful and idealized places from another time period. In Yeats's poem, it is the Byzantium of centuries past; for Silverberg's hero Charles Phillip and his female friend and love interest Gioia, it is the fiftieth century in the future. Both Charles and Gioia are mysteriously transported from the year 1984 to a far distant and depopulated earth, which has five beautiful cities. One is Byzantium, another Alexandria—all are mythic recreations of what these metropolises looked like in their heydays.
Both writers use beautiful imagery to describe their dreamscapes. Yeats's poem states that in Byzantium he wishes to become

such a form as Grecian goldsmiths make / Of hammered gold and gold enamelling / To keep a drowsy Emperor awake; / Or set upon a golden bough to sing . . .

Silverberg also uses vivid imagery as he describes Alexandria, recreated from its ancient Egyptian period, as containing

the wondrous, many-windowed lighthouse, seventh wonder of the world, that immense pile of marble and limestone and reddish-purple Aswan granite rising in majesty . . .

Both writers also focus on the theme of mortality versus immortality. The aging speaker in Yeats's poem longs to sail to Byzantium because he wants to gain immortality by becoming a beautiful work of art that will never die. In the future world of Silverberg's story, the inhabitants also never die, and yet Charles has to deal with anguish as his beloved Gioia begins to show she is aging.