It is well known that Abu Bakr was not nominated by the Prophet SAW, nor was Umar or Uthman. But was does Allah and Islam say about how a caliph is chosen? This is a simple analysis of some traditions from the School of Companions.
Narrated Abu Sa`id Al-Khudri:
The Prophet (ﷺ) said, “Allah never sends a prophet or gives the Caliphate to a Caliph but that he (the prophet or the Caliph) has two groups of advisors: A group advising him to do good and exhorts him to do it, and the other group advising him to do evil and exhorts him to do it. But the protected person (against such evil advisors) is the one protected by Allah.’ “
Sahih al-Bukhari 7198
It was narrated that ‘Aishah said:
“They say that the Prophet (ﷺ) made a will for ‘Ali, but he called for a basin in which to urinate, then he went flaccid suddenly (and died), so how could he leave a will?!” The Shaikh said: Azhar (one of the narrators) is Ibn Sa’d As-Samman.  Meaning, appointing him as the Khalifah.
Nisa’ee Vol. 1, Book 1, Hadith 33
Abu Bakrah said:
One day the Prophet (ﷺ) asked: Which of you had a dream? He then mentioned the rest of the tradition to the same effect, but he did not mention the word “disliked”. Instead, he said: The Messenger of Allah (ﷺ) was grieved about that. He then said: There will be a caliphate on the model of prophecy, then Allah will give the kingdom to whom he wills.
Sunan Abi Dawud 4635
The definition of Irony
‘Umar bin Khattab said:
“There are three things, if the Messenger of Allah (ﷺ) had clarified them, that would have been dearer to me than the world and everything in it: a person who leaves behind no heir, usury, and the caliphate.”
Vol. 4, Book 23, Hadith 2727 Sunan Ibn Majah
Interesting Choice of words
‘Irbad bin Sariyah (May Allah be pleased with him) reported:
One day, Messenger of Allah (ﷺ) delivered a very effective speech, as a result, eyes shed tears and hearts became softened. A man said: “O Prophet of Allah! It sounds as if this is a farewell speech, so advise us.” He (ﷺ) said, “I admonish you to fear Allah, and to listen and obey even if a black slave has been appointed as your leader. For whoever among you lives after me will see much discord. So hold fast to my Sunnah and the Sunnah of the Rightly-Guided Caliphs who will come after me. Adhere to them and hold fast to them. Beware of Bid’ah (in religion) because every Bid’ah is a misguidance.”
It is our belief that Al Mahdi AS was born to a Sudanese (black) slave lady.