Gemara

(Beraisa - R. Eliezer ben Yakov): I heard that Beis Din can lash or punish not according to Torah law. They do not intend to change Torah law, rather, to make a fence (to deter transgressors).

A case occurred in the days of the Yevanim, a man rode on a horse on Shabbos. Beis Din killed him. He did not deserve to be killed, but at the time it was necessary.

Sanhedrin 45b (Mishnah - R. Eliezer): We hang a man facing people, we hang a woman facing the beam;

Chachamim say, we hang only men, but not women.

R. Eliezer: Shimon ben Shetach hung women in Ashkelon!

Chachamim: He hung 80 in one day, even though we do not judge two capital cases in one day (it was due to an urgent need, it was not according to Halachah).

52b: A Bas Kohen was Mezanah. Rav Chama bar Tuvya burned her in a fire of sticks.

Rav Yosef: He made two mistakes. He erred about Rav Masnah's teaching (that the Pesilah for Sereifah is molten lead), and about a Beraisa:

(Beraisa): "U'Vosa El ha'Kohanim ha'Leviyim v'El ha'Shofet Asher Yihyeh ba'Yomim ha'Hem" - we judge capital cases only at a time when there are (Shoftim, i.e. the Sanhedrin in Lishkas ha'Gazis, near the) Kohanim.

Bava Metzi'a 83b: R. Elazar b'Rebbi Shimon found a king's official who used to seize thieves. R. Elazar told him to see who is drinking wine in the store and dozing at four hours of the day and investigate. If this cannot be attributed to staying up late or rising early to learn or work, he is a thief. The king heard about this and appointed R. Elazar to seize thieves.

R. Yehoshua ben Korchah objected vehemently to giving over Yisraelim to be killed. He did not accept R. Elazar's defense 'I eliminate the thorns from the vineyard!'

Rishonim

The Rif and Rosh (10:2) bring the Gemara (Yevamos 90b) verbatim.

Nimukei Yosef (DH Tanya): There were decrees against Mitzvos and Yisraelim were transgressing and Mitzvos were disgraced in the eyes of people.

Question (Nimukei Yosef Sanhedrin 16a DH Garsinan): Why does it say that Rav Chama erred about judging capital cases when there is no Kohen? Beis Din can punish not according to Torah law!

Answer (Nimukei Yosef): Only the Great Sanhedrin is authorized to do so. Even though Rav Huna cut off a man's hand, and the Reish Galusa was prepared to gouge out his eyes of a murderer, this is to give some of the Torah punishment. Only the Great Sanhedrin can give the full punishment.

Rebuttal (and Answer #2 - Hagahos ha'Bach 3): Even nowadays we give severe punishments when necessary at the time (Rivash 251)! It seems that Rav Yosef knew that Rav Chama did not intend for this, rather, to execute Torah law.

Question (Gedulei Terumah, brought in Birkei Yosef CM 2:3): Perhaps Rav Chama only made one mistake, i.e. he thought that any Beis Din may punish for Migdar Milsa! If Rav Yosef knew that there was no need for this, the Nimukei Yosef's question does not begin!

Answer (Birkei Yosef CM 2 DH v'Anochi and DH Emnam): It was known that such a severe punishment, burning the entire body, is not permitted for Migdar Milsa. However, the Nimukei Yosef connotes that the Great Sanhedrin can give the full punishment or even more, like the man killed for riding on a house. If so, perhaps Rav Chama's only mistake was to think that any Beis Din can do so! It seems that even the Great Sanhedrin would not need to do so when the person is Chayav Misah mid'Oraisa, for every Chiyuv Misah suffices to admonish people.

Rambam (Hilchos Sanhedrin 24:4): Beis Din can lash or kill someone who is not liable to receive lashes or death, not to transgress Torah law, rather, to make a fence for Torah. If Beis Din sees that people wantonly transgress a matter, they should fence and fix it as they see fit. This is a Hora'as Sha'ah (a temporary ruling). The Halachah is not fixed like this for all generations. A case occurred in the days of the Yevanim in which a man rode on a horse on Shabbos. Beis Din killed him. Shimon ben Shetach once hung 80 women in one day in Ashkelon. There was not proper interrogation of witnesses or warning or clear testimony. It was a Hora'as Sha'ah based on what he saw.

Sha'arei Yeshu'ah (cited in Birkei Yosef ibid., DH v'Chazah): The next Halachos in the Rambam say that at all times Beis Din may impose lashes and monetary fines and excommunicate as they see fit. He holds like the Nimukei Yosef, that Beis Din cannot kill nowadays. Rashi (Sanhedrin Sof 27a) says that the Reish Galusa (only) sought to remove Bar Chama's eyes because Misas Beis Din is Batel, but Beis Din can punish unlike Torah law. Rashi (45a DH she'Beis Din) explains that Beis Din can punish and even kill unlike Torah law. He refers to the Great Sanhedrin. Also the Rif (Bava Kama 34a) discusses a monetary fine of Rav Nachman, and says 'this teaches that even in Chutz la'Aretz we may impose such fines,' i.e. to exclude capital punishment.

Rebuttal (Birkei Yosef ibid.): I say that the Rambam holds like the Tur, that even nowadays Beis Din may kill. In Halachah 4 he cited the Gemara. In the next Halachos he explains that these powers are even nowadays. Rashi holds like the Rivash (251) that the Reish Galusa thought that gouging out Bar Chama's eyes would suffice. We do not rely on such a weak inference in the Rif's words.

Ran (Sanhedrin 27a DH Iy Vadai): Rashi's Perush is difficult. To punish unlike Torah law is even more severe and requires greater judges. How can they do so in Bavel, where they do not even have power to judge capital cases?! Rather, the Reish Galusa did not rely on the power of Beis Din, rather, on the power of a king to get rid of Resha'im.

Rambam (Hilchos Rotze'ach 2:4): A Melech Yisrael may decide to kill murderers and similar people who are not Chayav Misas Beis Din. Similarly, if Beis Din saw fit to kill them for Hora'as Sha'ah, if it was necessary at the time they may do as they see fit.

Ritva (Bava Metzi'a 83b DH Omar): R. Elazar acted without witness or warning and when there is no Beis Din. He was a Shali'ach of the king.

Birkei Yosef (ibid., DH Shavti): The Ritva determined that he did not rely on the power of Beis Din because he judged alone, based on estimation. Also, it seems that R. Elazar did so constantly, so it could not be a Hora'as Sha'ah.

Poskim

Shulchan Aruch (CM 2:1): Any Beis Din, even if it is did not get Semichah in Eretz Yisrael, if it sees that people wantonly transgress a matter (and it is necessary at the time) they can impose death or any other punishment, even if there is not full testimony. All their actions must be l'Shem Shomayim. Only a Gadol ha'Dor may do so, or Tuvei ha'Ir (the governors of the city) if Beis Din authorized them.

Bedek ha'Bayis (citing Rikanti citing Zohar Mishpatim 112): A judge who is meticulous to acquit Resha'im will die before his proper time. Beis Din should punish more than the Torah says to make a fence for Torah! A man once kissed an Eshes Ish, and Aba killed them.

Prishah (1): Even in Chutz la'Aretz, if it is necessary any Beis Din can kill someone who is liable according to Torah law. If the Tzibur accepted Beis Din upon itself, they can punish even more than Torah law. Since Rav Nachman imposed a fine in Bavel, even though we do not collect fines in Bavel, this shows that we do not distinguish between money, lashes and death.

Rema: This is the custom everywhere, that Tuvei ha'Ir in their city are like Beis Din ha'Gadol. They can lash, punish and make Hefker according to the custom. Some argue and say that Tuvei ha'Ir can only force the Tzibur to fulfill existing customs or what the entire Tzibur agreed to. In any case we follow the custom in the city, all the more so if the city accepted the Tuvei ha'Ir to do everything.

Tur (425): R. Natrunai Ga'on says that nowadays, Beis Din cannot lash or kill. It can only excommunicate. Perhaps he refers to according to Torah law. Surely, he does not disagree with R. Elazar, who says that Beis Din can lash or punish not according to Torah law to make a fence. In a Teshuvah, a Gaon says that on Purim a person merry with wine killed someone. They decided to lash and punish him for Migdar Milsa, lest people think that they can shoot arrows and say 'I was Shogeg'. We do not do so for an individual, only if there is a need for the Rabim.