GEHENNOM: loosely translated as ''hell''.
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"If people knew of the bitter punishments of Gehinom, they would fall on their faces and scream and they would not have any business whatsoever with matters of this world." - Rabbi Yehonason Eibshetz, Ye'aros Devash 1:2
Note: The potentially infinite sufferings of Gehinom from a benevolent G-d only make sense if man and his actions in this world are also infinitely important. Otherwise how could G-d punish so immensely for such insignificant acts? From learning about Gehinom we can get a glimpse of the greatness of our mission in this world and the enormous responsibility that lies on our shoulders.
The midrash says: Before a person is born a "candle" is put on his head (i.e. an angel teaches him the whole Torah) and he gazes from one end of the world to the other as written "When His candle would shine over my head" [Iyov/Job 29:5]. Just before birth, the angel takes him/her to Gan Eden and shows him/her the tzadikim sitting with their crowns on their heads.
And the angel says to him:
"Know who these people are that you are seeing. They were formed just like you in their mother's womb and were born into the world. They guarded G-d's mitzvos, and therefore merited this goodness. And soon you too will be born into the world and if you are meritorious and you guard the Torah you will have a place with them, otherwise you will sit elsewhere".
Afterwards, he is brought to Gehinom and he is shown the wicked which are beaten by angels of destruction using clubs of fire and scream 'voy, voy'. And the angel says to him:
"Know that these that are being burned, they were formed just like you and they were born into the world and did not guard G-d's mitzvos. Therefore they are punished and humiliated like this. And you will soon be born. Be a tzadik and don't be a rasha, in order that you live." [as it is written "And he taught me, and said unto me, 'Let your heart hold fast my words, keep my commandments, and live'" - Mishlei/Proverbs 4]
When the time comes to leave the womb, immediately the angel hits him and extinguishes his candle and pushes him out by force and he forgets everything he saw. It is because of this, that a baby cries (i.e.even though the baby forgot, his 'inner soul' remembers and he cries) immediately when it is born [Midrash in Rabbeinu Bechayei - end of Acharei Mos]
Throughout a person's life the Midda of Din (trait of justice) accuses him/her (in the Heavenly court) but it is not listened to. When the day of death comes it is listened to. [Vilna Gaon -Even Shlema ch.10]
At the time of death is the very great day of judgment. Generally G-d judges leniently, but for someone who was "ra l'brios" (evil to society), he is given the full measure of justice. And likewise for a haughty person.
The body and the 'nefesh' are judged for 30 days and the 'ruach' is judged for 12 months (Except for heretics, deniers of the Torah, Jews who abandon their religion, who stay there forever [see Rosh Hashanah 17a for a list of sins warranting punishments of eternal Gehinom (and not just 12 months)]
[everything below is from the Ramban's book Shaar HaGemul unless otherwise stated]
There are three entrances to Gehinom.
1. desert - "they [Korach, Dasan, Aviram and their families] descended with all their possesions alive to the she'ol (Gehinom)" - [Bamidbar 16:33]
2. sea - "from the belly i saw the she'ol" [Yona 2:3] when Yona was in the belly of the fish, it swam to the depths of the sea and showed him the entrance to Gehinom.
3. in Jerusalem as it says : "He has fire in Tzion and an oven in Jerusalem". and R. Yochanan ben Zakai said:"there are 2 palm trees in the valley of Ben Hinom and smoke rises between them - this is the entrance to Gehinom." [Eruvin 19]
A person must pass through all three "landscapes" after death. [Vilna Gaon on Mishlei 3:24]
The River of Fire ["Nahar Dinur", Daniel 7:10] separates between the mystical Land of Israel on high and the mystical "chutz l'aretz" (diaspora) just like the Jordan river separates the land of Israel from the diaspora below. [Vilna Gaon - ES 10:16]. (this means the Dead Sea which is the end of the Jordan river and the lowest place on earth (by far at 418m below sea level), corresponds to Gehinom which is the end of Nahar Dinur and the "lowest place" in the mystical worlds.)
Generally speaking, every Biblical and Rabbinic transgression requires a sentencing in Gehinom (unless one repents before death, in which case he is forgiven completely). Some examples of sins which merit Gehinom in the other levels [from Zohar Chadash Ruth 79a quoted from Reishis Chachma - Shaar Yira Ch.13] :
Level 1) someone who interrupts his Torah study to engage in idle chatter, someone who doesn't honor talmidei chachamim, someone who curses a deaf person or the like, someone who says good things about someone in front of his enemy (causing him to say lashon hara).
Level 2) someone who honors himself through putting down someone else, someone who knows his friend is going to stumble in halacha and he doesn't tell him and they're both in the same city, someone who has a shul in his city and doesn't go there to pray, someone who lifts his hand to hit his friend even though he doesn't hit him, someone who insults his friend and causes him embarassment.
Level 3) scholars who are arrogant in their Torah study, someone who judges others negatively (l'kaf chova), lends money with ribis, doesn't say amen after someone's blessing, interrupts his davening and talks, an old scholar who forgot his Torah learning (through neglect)
Level 4) arrogant people (gasei ruach), someone who speaks harshly to the poor and the downtrodden, someone who sees a poor man in a tough situation and doesn't lend him money, someone who oppresses his employee (oshek schar sachir), a man who wastes seed (motzi zera lbatala), someone who has relations with a gentile or a nidda, a judge who corrupts justice or takes a bribe. [from Zohar Chadash Ruth 79a quoted from Reishis Chachma - Shaar Yira Ch.13]
(Also, gentiles who did not keep the 7 mitzvot of Bnei Noach will be sentenced to Gehinom, even if they had no education whatsoever in the matter. The gentile will respond to the Heavenly court screaming "how could I have known!?" which on the surface seems like a good claim. But it will not be accepted. The reason is that every creature and every phenomena in the world reflects intelligent design of infinite proportions. Any person who is not insane knows in his heart that there must be a Designer. This obligates him to question and search out the truth with all his heart, as to why he was created and what his purpose in this world is. If he doesn't do it, it is only because he is entangled in his desires and does not want to know. For this he/she will be sentenced.[Kovetz Ma-amarim by Rav E.Wasserman - sec. Emuna.]
THE GREAT DAY OF JUDGMENT
Originally G-d wanted to create the world with justice, whereby a sinner would be destroyed immediately and not be given a second chance (according to strict justice, one who sins no longer deserves to live). He saw the world could not endure and merged justice with mercy to give sinners a chance to repent. This is why this world seems to have no justice and evildoers roam freely.
In the future, will be the 'great day of judgment'. Everyone who ever lived must, in turn, stand individually in front of G-d while all of humanity watches. All of his life is reviewed on a large movie screen, including all of his actions, words, thoughts, in front of all of humanity (but if he does teshuva, that part of the tape is erased. The final accounting of all the consequences of his actions relative to other people and all descendants will also be examined and taken into account as it says "the end of the matter all is heard" [Koheles 12:13]. Then each and every person will receive the full measure of justice without any mercy or any favoritism as G-d had originally intended to create the world [Yearos Devash 1 Derash 6].
Rabbi Yehonosan Eibshetz, zt'l explains that all the suffering a person has while alive in this world is not in the category of punishment. It is only there to wake him up in order that he mend his ways. Similarly, he says the sufferings of Gehinom are also not in the category of punishments. Their purpose is only to clean and purify the soul from the sins which contaminated it in order that it be fitting to behold the face of the King on the "Great Day of Judgment". The main punishment will be meted out then (unless one repented before death).
One who learns to overlook the bad things that people do to them, will be forgiven for all their sins (measure for measure). [Talmud Yoma 23a]
"Be concerned that you do not offend, not that you are not offended" - [Mildred N. Ryder]
If one observes Shabbos properly, then G-d forgives him for all of his sins. [Talmud Shabbos 118b].
Whoever recites the Shema and is careful with the pronunciation, Gehinom will be cooled down for him (assuming he is sentenced to spend some time there) [Talmud Berachos 15b]
"The fire of Gehinom has no power over those who learn Torah" - [Talmud Chagigah 27a]
Someone who stares at women for pleasure, even if he has Torah and good deeds like Moshe Rabeinu, it will not save him from Gehinom [Berachos 61]
Tzedaka saves a person from Gehinom - [Bava Basra 10a]
Someone who visits a sick person and sees to his needs, will be saved from Gehinom - [Talmud Ta'anis 7b]
"Whoever gets angry all types of Gehinom rule over him" - [Talmud Nedarim 22] "The fire of Gehinom has no power over those who are free from anger" - [Sefer Maalos HaMidos beginning of Maalas HaRatzon]
Rabbi Yisrael Salanter, zt'l would bring his hand very close to the havdala candle every motzei shabbos to remind himself of the fires of Gehinom.
There is also a parallel Gehinom of snow. When one refrains from transgressing the negative commandments in the Torah, it makes a protective "garment" called "shanim" (lit. "years" since there are 365 days/year and 365 negative mitzvot) which protects from the snow blizzard there. This is alluded in the Friday night "Aishes Chayil" song: "lo sira beisa mi'shaleg ki kol beisa lavush shanim" - her house will not fear snow because her whole house is 'clothed' in 'shanim'. [Vilna Gaon on Mishlei 31:21-22]
"And you will return to Hashem your G-d" - [Devarim 30:2]"
Nothing stands in the way of teshuvah [Rambam Hilchos Teshuva 4:1]. Even if one transgressed throughout his entire life but repented on the day of his death and died in repentance, all his sins are forgiven." [ibid 2:2]
Said The Holy One blessed be He: "My children open for Me one opening of repentance the size of a pin prick and I will open for you openings through which even wagons can enter." [Shir Ha'shirim Rabba 5:3]
Without teshuvah the world could not endure. Without teshuvah man could not but despair, crushed by the burden of his errors. Torah is the foundation of the universe, it assures and sustains its existence. Teshuvah ensures its survival.
The first step (in teshuva) is to drop the burden of the past completely from your shoulders. Start anew as if you were born today...[Rabeinu Yona - Yesod HaTeshuva] "The shame and regret that the soul feels from one transgression is far worse than all the pain of this world. One act of getting angry, or hurting someone, or being depressed, or wasting time... is a relentless eternity of pain.
Now for some good news. The pain of Gehinom is nothing compared to the reward of one mitzvah. In other words, if you experienced the pain of all the Gehinom of every person since the beginning of time, it would still be worth it to gain the reward of one mitzvah."
The main purpose of life is not to refrain from evil but rather, to do good. [R.Avigdor Miller zt'l].