At what time does the fast of asrah beteves begin on Sunday morning in Jerusalem? And what time does it end? What are the reasons for this fast?
The reason for the fast on Asara B’teves is because this was the day that started the process of the destruction of the Bais Hamikdash, as the gemorah Rosh Hashana, and in Yechezkel 24. This fast in a way is more serious even than T’bav, because technically if the fast would fall on Shabbos we would fast on it, even though we don’t fast on T’bav when it falls on Shabbos, since it was the start of all the problems.
Although the fast officially start from Alos Hashachar, when a person goes to sleep for the night, he may not eat anymore, unless he stipulates, (even if it was only mentally) that he wants to eat early in the morning. Drinking in any case is permitted.
The fast in Yerushalayim starts on Sunday at 5:23, and it ends 5:22.
Rambam Hil. Taanis 5-2, Avudraham Seder tanaios, Bnei Yisoschar Mamarei teves 14. Rema 564–1. Regarding thinking the stipulation see Luach Ahavat Shalom pg. 228 ftnt. 60