It is narrated from Hazrat Aisha (may Allah be pleased with her) that the Prophet (peace and blessings be upon him) passed away in such a state that the Prophet (peace and blessings be upon him) had not explicitly appointed anyone as his successor. If the Prophet (peace and blessings be upon him) had done so, he would have appointed either Hazrat Abu Bakr (may Allah be pleased with him) or Hazrat Umar (may Allah be pleased with him) as his successor.