WHAT IS FORBIDDEN ON THE 10TH OF AV? [Tish'ah b'Av: Motza'ei: Isurim]
Gemara
(Rav Asi): If Ploni's relative died and was buried on the 14th of Nisan, Ploni may eat Pesach but not other Kodshim that night. (Aninus of the night after the death is mid'Rabanan. Chachamim did not decree regarding Pesach);
If the death was on the 13th and the burial was on the 14th, he may eat any Kodshim that night. (Chachamim did not decree Aninus on the night following burial.)
Ta'anis 29a (Beraisa): On the ninth of Av, close to dark, the enemy lit the fire, and the Beis ha'Mikdash burned the entire day (of the 10th).
(R. Yochanan): Had I been there, I would have fixed the fast on the 10th, for the Heichal burned mostly on the 10th.
Rabanan fixed the fast on the ninth. They hold that the beginning of the punishment is primary.
Eruvin 41a (Beraisa - R. Eliezer b'Ribi Tzadok): Once, Tishah b'Av fell on Shabbos, and the fast was Nidcheh (postponed) to the 10th. My family did not complete the fast, for we descend from Sin'av ben Binyamin (a family that used to bring wood for the Mizbe'ach on the 10th of Av). It is Yom Tov for us.
Rishonim
Tur (OC 559, Mordechai Ta'anis 630, Hagahos Maimoniyos Hilchos Ta'anis 5:8 citing Maharam): A case occurred in which Rabbeinu Ya'avetz was a Ba'al Bris on Tish'ah b'Av postponed until Sunday. Based on Eruvin 41a, he prayed Minchah early in the afternoon, bathed and did not finish the fast, for it was his Yom Tov.
Beis Yosef (559 DH u'Ba'al): It seems that 'he was a Ba'al Bris' means that he was the father of the baby. However, the Mordechai (Ta'anis 635) discusses Ba'alei Bris. Perhaps this includes the Mohel (one who circumcises) and Sandek (who holds the baby). Tashbatz cites a case in which a Bris was on Tish'ah b'Av Nidcheh to Sunday. R. Yakov ben R. Yitzchak (Ya'avetz) was the father. He commanded to pray Minchah Gedolah (shortly after noon). He and his Ba'al Bris then bathed, did the Bris, and ate their fill, and did not finish the fast with the Tzibur. We permit (Kohanim serving in the Mikdash to cut hair and launder) on Thursday due to Kevod Shabbos (Ta'anis 15b), so all the more so for a Ba'al Bris. This implies that Ba'al Bris is the Mohel or Sandek. It is their Yom Tov, just like for the father. Hagahos Ashri (Mo'ed Katan 3:37) connotes that it is only the Sandek. It seems that the Mohel is no worse than the Sandek.
Maharil (125): If one's custom is not to eat meat or drink wine on the day after Tish'ah b'Av, or to fast the ninth and 10th (based on Ta'anis 29a), and Tish'ah b'Av was Nidcheh to Sunday, so the second day is the 11th, must they abstain from meat and wine or fast on Monday? The Yerushalmi brings that R. Avin used to fast the ninth and 10th, but he would not fast two days when Tish'ah b'Av was Nidcheh to Sunday, for the 10th is an excessive stringency. Even on the 10th itself we are lenient, like the case of Rabbeinu Ya'avetz, who bathed and did not finish the fast when he was a Ba'al Bris (Or Zaru'a 2, Aveilus 440). If so, there is no source to be stringent on the 11th. The Mordechai (Pesachim Sof 543) says that Rashi was stringent when Erev Pesach was on Friday to burn Chametz before six hours. He decreed lest one delay after six hours in other years. That was due to concern for a Torah Isur, lest one not do Bitul in time. Here it is only a custom. One who refrains from meat and wine for the entire three weeks refrains also on Motza'ei Tish'ah b'Av. This is even if the fast was Nidcheh. In many fasts for Teshuvah, we do not eat meat or wine the following night.
Poskim
Shulchan Aruch (OC 558:1): On the ninth of Av, towards evening, they set fire to the Heichal, and it burned until Shki'ah of the 10th. Therefore, it is a proper custom not to eat meat or drink wine on the night and day of the 10th.
Beis Yosef (DH v'Isa): The Avudaraham says that the Rosh would not eat meat on the night of the 10th. Hagahos Maimoniyos says that some refrain from meat and wine until midday of the 10th.
Teshuvas Maharshal (92): We refrain from meat on the 10th, like the Tur says. Also bathing is forbidden. Minhagim (of Mahara Tirana) praises refraining from meat and wine at night and during the day of the 10th, but one may cut hair and launder immediately after the fast; the Gemara concludes like this. Do not heed this. Our custom is not to to eat meat or drink wine on the 10th, so also these (cutting hair and laundering) are included. How can we oppose the Gemara, which rules like R. Meir, that Aveilus is only until the fast? The custom of most of Yisrael in Galus is to refrain from meat and wine from Rosh Chodesh. All Yisrael accepted this, so it became obligatory, like the Rashba says. The Gemara permits meat and wine on Erev Tish'ah b'Av before the last Seudah before the fast, but one who eats meat in any place where the custom is to forbid breaches a fence; "one who breaches a fence will be bitten by a snake." The 10th is the neighbor of the ninth, and the Mikdash burned primarily on the 10th. It is no less than the days from Rosh Chodesh until the ninth. The custom is to refrain from meat and wine during these days, even before the week of Tish'ah b'Av. The Gemara decreed only what the Tzibur can fulfill. Nowadays that people are accustomed and accepted an Isur of meat, wine and bathing (from Rosh Chodesh), for mere pain to remember the Churban and sadden the heart, all the more so this applies to the 10th. Early Chachamim were stringent to fast on the 10th, due to R. Yochanan's opinion. However, when Tish'ah b'Av is Nidcheh to Sunday, everything is permitted after the fast, for the 10th already passed. I explicitly saw so regarding meat and wine. However, the Beis Yosef forbids one who is accustomed not to eat meat or drink wine after the fast. He says that this is not due to R. Yochanan, rather, due to the stringency of the fast and Aveilus of the day. It is part of Bein ha'Metzarim. This is not a proper reason. However, I agree (with the law), for Sefer Chasidim says that it is proper not to eat meat or drink wine before or after a fast. If so, all the more so regarding Tish'ah b'Av, for which it was fitting to stop during the day before the fast, we should refrain from meat and wine on the night after the fast.
Bach (1): Also my Rebbeyim decreed on the Tzibur to forbid meat and wine at night even when Tish'ah b'Av was Nidcheh, but then meat and wine are permitted on Monday, and all the more so haircuts, laundering and bathing. Maharshal (on the Tur) forbids haircuts, laundering and bathing on the 10th, unlike Minhagim. Since meat and wine are forbidden at night, one may not slaughter until after the Ta'anis, unlike Teshuvas ha'Rashba (306). One may permit Shechitah (from midday on Tish'ah b'Av) when the fast is on Thursday, for the needs of Shabbos.
Taz (1): For 40 years, the custom is not to eat meat or drink wine the night after the fast. Before this, they ate meat.
Gra (DH Mipnei): Letter of the law, all is permitted immediately after the fast. A Tosefta says so. The Yerushalmi says that they would announce that people may cut hair.
Birkei Yosef (2): Sefer ha'Kavanos says that R. Chaim Vital would eat (meat) the night after the fast when it was Nidcheh. Pri Chodosh says that there is no reason to forbid after the fast.
Ha'aros on Birkei Yosef (1): The Birkei Yosef did not give his own opinion, for he did not want to decide the issue. Why would R. Chaim Vital eat meat?! We must say that it is because it is also a time of consolation, for Moshi'ach is born on Motza'ei Tish'ah b'Av. He ate meat due to this Simchah.
Mishnah Berurah (2): Anyone invited to a Seudas Mitzvah may eat meat on Motza'ei Tish'ah b'Av, even if he is not a relative. The night is more lenient than Rosh Chodesh Av. According to the Gemara, there is a little Aveilus from Rosh Chodesh; we diminish Simchah and business. Letter of the law, all is permitted after the fast. Keneses ha'Gedolah says that it is good not to have relations on the night of the 10th, unless it is Leil Tevilah (the night she immerses), or if he will be going away or returned home.
Kaf ha'Chayim (7): Doctors say that one should not have relations after a fast, for he became weak. However, if it is Leil Tevilah, relations is a Mitzvah, so "Shomer Pesa'im Hash-m" (Hash-m guards those who do not know to guard themselves).
Kaf ha'Chayim (8): Those who refrain from blessing Shehecheyanu during the three weeks should refrain also on the 10th.
Kaf ha'Chayim (2): The Bach derives from the Tur that one should eat only what is needed to revive himself. The Taz permits other foods, for there is no Simchah without meat.
Kaf ha'Chayim (4): One may eat a food cooked with meat, and bless Birkas ha'Mazon over wine if he does so the entire year.
Kaf ha'Chayim (6): The Isur is to bathe in a bathhouse, but other washing, which is forbidden on Tish'ah b'Av, is permitted.
Rema: Some are stringent only until midday.
Mishnah Berurah (3): Likewise, one may not bathe in a bathhouse, cut hair, or launder until midday. If the 10th is Erev Shabbos, all this is permitted for Kevod Shabbos.
Kaf ha'Chayim (10): The Bach says that it is proper for a Chacham or pious person to be stringent the entire day. Also Eliyahu Rabah, Machazik Berachah and Sha'arei Teshuvah bring this.
Rema: If Tish'ah b'Av is Nidcheh to Sunday, one may eat meat or drink wine on Monday, but Sunday night is forbidden due to the Aveilus of the day.
Mishnah Berurah (4): We forbid only meat and wine, but all permit cutting hair.
Mishnah Berurah (5): We are stringent on the following night only due to the Aveilus of Tish'ah b'Av. It is like Bein ha'Metzarim. One should not be stringent about this for other fasts.
Kaf ha'Chayim (11): If a woman gave birth more than seven days ago, even though she fasts, she need not be stringent about meat and wine the following night, especially if Tish'ah b'Av was Nidcheh.
Rema (334:26): One who was Mechalel Shabbos must fast 40 days on Monday and Thursday, and not eat meat or drink wine.
Taz (20): He may not eat meat or drink wine after the fast, like we find on the night after Tish'ah b'Av. The Rema said that this is due to Aveilus of the day.
Mishbetzos Zahav: Eliyahu Rabah says that this is because the fast is in place of a Korban, and regarding Korbanos the night follows the day.
Igros Moshe (OC 3:88): The Magen Avraham says that the Rema's stringency on the night after a fast that was Nidcheh is due to the fast. Really, it is due to the Aveilus of the day. Even though an Avel may eat meat or drink wine, the Rema means that Tish'ah b'Av is like Aninus. The night after death, an Onen may not eat Kodshim, even after the burial. Even though an Avel is forbidden only if burial was the day of death, regarding Aninus of the Rabim (Tish'ah b'Av), Chachamim were stringent to forbid meat and wine the following night. After the Churban, Perushim wanted to abstain from meat, for it used to be offered in the Mikdash (Bava Basra 60b). R. Yehoshua refuted them. If so, we would need to refrain also from bread and water! R. Yishmael ben Elisha said that we should have decreed not to eat meat and wine, but we do not make decrees that the Tzibur cannot endure. What did he add? He taught that we should have decreed due to Aninus, for it is as if our Mes is in front of us, but the Tzibur cannot fulfill this. Toras ha'Shelamim (YD 185:10), Eliyahu Rabah and Mishbetzos Zahav say that the fast is in place of a Korban, and regarding Korbanos the night follows the day. This is wrong. We do not find any fast in which the night follows the day. Perhaps Mishbetzos Zahav refers only to a fast that is solely for the sake of Teshuvah.