This is a partial transcript from a YouTube video by Ajahn Brahm called Seven Steps to Heaven (and One Beyond). (the link skips directly there).
There is a lot in this video besides this section, but this is a pretty important point.
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Great question.
Can you be addicted to being in the Jhanas? The answer is yes.
It's stated in the Pāsādika Sutta of the Dīgha Nikāya.
If anyone asks you monks and nuns can you be addicted to the pleasures of the jhanas ... you should answer ... yes.
... because you are telling the truth.
Now what happens to you, if you are addicted to the pleasures of the jhanas?
Only four things can happen to you if you are addicted to the pleasures of the jhanas: stream winning, once returning, non-returning, and full enlightenment.
This is the referenced text in DN 29
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“It’s possible that wanderers of other sects might say, ‘Living devoted to these four devotions to pleasure, friends, what fruits, what rewards can be expected?’
“The wanderers of other sects saying that are to be told, ‘Living devoted to these four devotions to pleasure, friends, four fruits, four rewards can be expected. Which four?
“‘Friends, there is the case where a monk, with the wasting away of (the first) three fetters, is a stream-enterer, certain, never again destined for the lower realms, headed for self-awakening. This is the first fruit, the first reward.
“‘Further, friends, the monk—with the wasting away of (the first) three fetters, and with the attenuation of passion, aversion, & delusion—is a once-returner; who, on returning only once more to this world, will make an ending to stress. This is the second fruit, the second reward.
“‘Further, the monk—with the wasting away of the five lower fetters—is due to arise spontaneously (in the Pure Abodes), there to totally unbind, destined never again to return from that world. This is the third fruit, the third reward.
“‘Further, the monk—with the ending of effluents—enters & remains in the effluent-free awareness-release & discernment-release, having directly known & realized it for himself right in the here & now.
“‘Living devoted to these four devotions to pleasure, friends, these four fruits, these four rewards can be expected.’