Two-day Yom Kippur:
Some [in the Diaspora] are stringent to keep two days of Yom Kippur. This has the status of a vow. Practically, it is not proper to do so.
 Admur 624/10
 The reason why we do not need to keep two days of Yom Kippur: a) There is worry of danger; b) Now since we are expert in the days of the month we know for certain that the 1st day is Yom Kippur, and the same for the 1st day of any holiday, and it is only due to Minhag Avoseinu which kept two days in times they did not know the correct days of the month that we keep two days of other holidays, however by Yom Kippur even they did not keep two days back then due to the worry of danger, and therefore there is no point in being stringent. [ibid]