1) The Prophet (PBUH and HF) said: "Even if the entire duration of the world's existence has already been exhausted and only one day is left (before the day of judgment), Allah will expand that day to such a length of time, as to accommodate the kingdom of a person from my Ahlul-Bayt who will be called by my name. He will fill out the earth with peace and justice as it will have been full of injustice and tyranny (by then)."
References:
Sahih al-Tirmidhi, v2, p86, v9, pp 74-75
Sunan Abu Dawud, v2, p7
Musnad Ahmad Ibn Hanbal, v1, pp 84,376; V3, p63
2) The Prophet (PBUH and HF) said: "al-Mahdi is one of us, the members of the household (Ahlul-Bayt)."
Reference: Sunan Ibn Majah, v2, Tradition #4085
3) The Prophet (PBUH and HF) said: The Mahdi will be of my family, of the descendants of Fatimah (the daughter of the Prophet (PBUH)).
References:
Sunan Abu Dawud, English version, Ch. 36, Tradition #4271 (narrated by Umm Salama, the wife of the Prophet)
Sunan Ibn Majah, v2, Tradition #4086
4) The Prophet (PBUH and HF) said: "We (I and my family) are members of a household that Allah (SWT) has chosen for them the life of the Hereafter over the life of this world; and the members of my household (Ahlul-Bayt) shall suffer a great affliction and they shall be forcefully expelled from their homes after my death; then there will come people from the East carrying black flags, and they will ask for some good to be given to them, but they shall be refused service; as such, they will wage war and emerge victorious, and will be offered that which they desired in the first place, but they will refuse to accept it till they pass it to a man from my family (Ahlul-Bayt) appears to fill the Earth with justice as it has been filled with corruption. So whoever reaches that (time) ought to come to them even if crawling on the ice/snow since among them is the Vice-regent of Allah (Khalifatullah) al-Mahdi."
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