So a couple of days ago, I read again the Indonesian and English versions of Bidayatul Mujtahid and I found out in the Jinayat (penal offenses) section, Zina (unlawful intercourse) sub section, that having an intercourse with your own slave (whether you're marrying or not marrying the slave) is not considered as a penal offense. In fact, Ibn Rusyd states in such sub section that this has been agreed by all of the Islamic legal scholars (as of his time). The sub section also discusses certain other issues such as the legality of having a sexual intercourse with other person's slave (with the master's consent), or whether a father is free to have a sexual intercourse with his son's slaves or a man to have a sexual intercourse with his wife's slaves. Although Ibn Rusyd recorded that Islamic legal scholars were still in debates on the validity of these actions, several of them have already considered those acts as permissible without the necessity of imposing any penal sanctions.
Upon reading this, I quickly understand that slavery is indeed not prohibited under classical Islamic Law. The legal logic is simple: you can't validly have a sexual intercourse with your slave if slavery is legally prohibited. This is also supported with the fact that some scholars allow a person to enjoy other person's slaves with prior approval on the basis of asset's transfer! On technical legal issues, I salute these classical scholars for being innovative, but isn't that mean that slavery still existed even 600 years after the birth of Islam and people still think it as an ordinary legal action?
Now I wonder, if we know that slavery is valid and permissible under Islamic Law, and the Koran never says that it is prohibited, nor condemns the act, can we now prohibits slavery? Under what basis? That this is a law that should be changed in accordance with the situations and conditions? Why can't we do the same with other Islamic law subjects? If we prohibit slavery, can we be considered as breaching God's rules by prohibiting things that have been declared as permissible?
As a separate note, you might be interested to know that modern scholar like Wahbah Az-Zuhaili still allows slavery of women and children in terms of war prisoner to the extent that they can be distributed as war's spoil (ghanimah). You can refer to his discussion in Fiqih Islam Wa Adillatuhu, General Fiqh Section, Jihad - War Prisoner sub section (it's in the 8th book of his book's Indonesian version).
Interesting issues to be followed up. Let's see whether I can finish my research during my study at University of Chicago.