Repentance in the Torah (5 books)
There is a misconception that the idea of repentance without blood does not appear in the Chumash.
It is true that "empty repentance" does not appear in Torah which is basically a formula based repentance.
Forgive me G-d for I have sinned or some sinner's prayer or confession, or surrendering all etc
This is because the Christian notion of sin and repentance is separate from the act of having broken a Law (which is the case with Torah).
In other words, in Torah repentance literally means a "returning" to the Law while in Christianity it means confessing to a prohibition that is either specified in the NT or some social misconduct (against what has socially been deemed immoral).
Examples of complete repentance (teshuva) in Torah without blood and applicable today.
Deut 30: 1-3
1 And it shall come to pass, when all these things are come upon thee, the blessing and the curse, which I have set before thee, and thou shalt bethink thyself among all the nations, whither the LORD thy God hath driven thee,
and shalt return (Shavta~Teshuva) unto the LORD thy God, and hearken to His voice according to all that I command thee this day, thou and thy children, with all thy heart, and with all thy soul;
that then the LORD thy God will turn thy captivity, and have compassion upon thee.
(please note that this is describing Israel during exile (repenting) turning back to Torah and being accepted without a sacrifice or a temple.
30 When you are in distress and all these things have happened to you, then in later days you will return (Shavta~Teshuva) to the Lord your God and obey him.
In other words repentance always must be accompanied by actions IE a returning to the Law and not just acknowledging that one is not perfect and needs someone to erase their ability to continue sinning (in a spiritual sense).
I believe these two methods of repentance are mutually exclusive, one washes out the other, they both can't exist in the same belief system.
This post is in no way stating that Christians lead immoral lives or are in anyway less ethical than Jews but rather that Christians pick and choose what is prohibited to them, mainly only focusing on the ethical precepts of the Law and completely forgoing the ceremonial precepts when the Torah itself never makes a distinction between the two.