Is there an authentic hadith that mentions the awaited Mahdi and his characteristics, and that he will appear at the end of time, and in which book can this hadith be found?

A Muslim must believe in what is stated in the Quran and Sunnah (definition), including the signs of the Hour and the emergence of the Mahdi, who will fill the earth with justice and during whose time blessings will abound. Authentic hadiths have indicated the emergence of the Mahdi, and that he will be from the Prophet’s household (peace be upon him), and his name will coincide with the Prophet’s name (peace be upon him), and his father’s name will coincide with the Prophet’s father’s name (peace be upon him). He will rule for seven years, and Allah will prepare him in a single night. During his time, blessings will emerge, and he will give away much wealth. Jesus son of Mary will descend during his time and pray behind the Mahdi. These hadiths indicate widespread transmission (tawatur) and certain knowledge of the Mahdi's appearance.