The first conceit, the extended metaphor in "The Sun Rising," is the speaker's treatment of the Sun as pedantic, annoying interruption. In the first stanza, the speaker chides the Sun, telling it to go wake up schoolboys and hunters. The speaker, in bed with his lover, does not want to awake or have to leave the bed. Then to underscore his point that the Sun is an unwelcome intruder, the speaker notes the Sun's (and Time's) irrelevance because their love is beyond the confines of time.
Love, all alike, no season knows nor clime,
Nor hours, days, months, which are the rags of time. (9-10)
In this dramatic monologue, Donne uses apostrophe, a figure of speech in which the speaker addresses an abstract idea, absent person, or personified object. In this case, the speaker addresses the personified Sun. The poem is narrated in the present tense as the Sun rises. This poem is an example of hyperbole, an exuberant exaggeration of the speaker's love, the second extended metaphor.
The rhyme scheme for all three stanzas is abbacdcdee. Some of the lines are short and this accentuates the speaker's monologue of scolding the Sun. The increases the intensity of his voice and establishes the Sun's personification.
In the second stanza, the speaker flatters the Sun, but follows up by mocking its supposed power, claiming he can eclipse the Sun's light with a wink. The speaker continues his mockery and continues praising the love between he and his mistress. He claims that his love is so grand that all the spice, wealth, and royalty of the world "here in one bed lay."
In the third stanza, the speaker's glorification of his love with his mistress reaches new heights. The poem has two extended metaphors. One is the personified Sun as an annoying and pretentious interruption. And, ironically, the speaker is also pretentious in the praise of his love which he claims is, at least metaphorically, worth all the value in the world. She, his lover, is "all states" and he is "all princes." And there is nothing else. Everything else is just a copy of themselves.
The speaker finally invites the Sun to shine on them. One could argue that the speaker is overdoing the glorification of his love. One could also argue that he is just so in love that he doesn't want it to end; he does not want to be reminded of the passage of time (which is the Sun's job, rising and setting). For the speaker, the entire world is their bedroom. If the Sun shines on them in that room, it shines everywhere. Their love is a world all by itself. Since this love is timeless, it cannot be disturbed by the Sun's indications of the passage of time. In this respect, the speaker is not merely flaunting his love in spite of the Sun. He is praising the richness of the intimate experience.