One halakha that is dependant on the local custom is whether or not one can work on the fast day of the Ninth of Av, which commemorates the destruction of both the first and second Temples. According to the Mishna, even in places where the custom was to permit people to work on Tisha b’Av, Torah scholars refrained from working. Rabban Shimon ben Gamliel taught that it would be appropriate for everyone to consider himself a scholar with regard to this custom, i.e. that anyone who can, should refrain from work on the fast day.
Most of the special rules and regulations that apply on the Ninth of Av stem from traditions of aveilut – mourning. Just as someone who is in aveilut for a parent refrains from wearing leather shoes, engaging in sexual relations or learning Torah, similarly the community that is in mourning for the Temple refrains from these activities. Rabbi Shlomo Adani in his Melekhet Shlomo points out that the Sages did not establish work as one of the things that is forbidden on Tisha b’Av, even though someone who has a personal aveilut does not work, because the communal mourning over the Temple is aveilut yeshana – it is commemorative mourning over a historical event, not a recent one.
In the Gemara, Shmuel rules that the only true ta’anit tzibur – communal fast – in Babylon is Tisha b’Av. The other fast days do not begin in the evening, nor do they encompass other rules aside from the fast itself. This also indicates that the fast days enumerated in Massekhet Ta’anit on the occasion of drought, will never be established in the Babylonian exile.
The rishonim differ in their explanations of Shmuel’s ruling. Rashi explains that in Babylon there was no need to establish fast days for drought, since most of the local water needs were supplied by the Tigris and Euphrates rivers. The Me’iri adds that the ruling applies to other locations in the Diaspora, whose traditions are modeled after Babylon, even if there is a need for rain in those places. The Ra’avad argues that Shmuel intended that his ruling apply to all Diaspora communities, because the people in those communities were weak from their travails and the Sages desired to lighten their burdens regarding fast days. According to the Ramban, the Diaspora communities are not considered a true tzibur, they are seen as a group of individuals, so any decision to establish a public fast would not have the full stringencies of a ta’anit tzibur.