Mut'ah is a special marriage, temporary in essence with a minimum of three days (buk
5119), where the husband and wife sets in advance the duration of said marriage (
4:24, especialy the tafsir of ibn Kathir). It was forbidden by Mohamed (mus
1405f). What is the difference with prostitution? Can Mohamed forbade what was hallal in the Coran? Is it possible for the prophet to abrogate the Quran?
And [also prohibited to you are all] married women except those your right hands possess. [This is] the decree of Allah upon you. And lawful to you are [all others] beyond these, [provided] that you seek them [in marriage] with [gifts from] your property, desiring chastity, not unlawful sexual intercourse. So for whatever you enjoy [of marriage] from them, give them their due compensation as an obligation. And there is no blame upon you for what you mutually agree to beyond the obligation. Indeed, Allah is ever Knowing and Wise. - Quran An-Nisa(The Women) 4:24 (islam)
Iyas b. Salama reported on the authority of his father that Allah's Messenger (ﷺ) gave sanction for contracting temporary marriage for three nights in the year of Autas 1847 and then forbade it. - Hadith Muslim 1405f (islam)
Book 16, Hadith 21
Book 8, Hadith 3251
Allah's Messenger (ﷺ)'s said, "If a man and a woman
agree (to marry temporarily), their marriage should last for three nights, and if they like to continue,
they can do so; and if they want to separate, they can do so." I do not know whether that was only for
us or for all the people in general. Abu `Abdullah (Al-Bukhari) said: `Ali made it clear that the
Prophet said, "The Mut'a marriage has been cancelled (made unlawful). - Hadith Al Bukhari 5119 (islam)
Book 67, Hadith 55
Vol. 7, Book 62, Hadith 52
I heard Ibn `Abbas (giving a verdict) when he was asked about the Mut'a with the women, and he
permitted it (Nikah-al-Mut'a). On that a freed slave of his said to him, "That is only when it is very
badly needed and women are scarce." On that, Ibn `Abbas said, "Yes." - Hadith Al Bukhari 5116 (islam)
Book 67, Hadith 53
Vol. 7, Book 62, Hadith 51