What does "chayav b'dinei shamayim" mean?

I see a number of places in Bava Kamma where it uses the phrase "חייב בדיני שמים" - obligated by the law of heaven. What does that mean?

Most people tell me it means, you don't have to pay, but you'll somehow be punished for the damage you did. Is that correct?

By the way, is it okay if I don't post by name?

I heard from my rebbi R' Zvi Berkowitz shlit"a that חייב בדיני שמים means that you absolutely have to pay. If you would ask a Rav, that is what he would tell you: You did damage, the Torah requires you to pay for it. However, the payment is not collectible in court (אינו חייב בדיני אדם); beis din will not come into your house and take your chairs to give to the victim. That's the difference from most of the laws in Bava Kamma.

And sure, it's fine to post under any username; on the internet today, it may sometimes be prudent. See the FAQ https://gemaraboards.forumotion.com/faq
You, for example, are really me under an assumed name - I'm testing the software.

Michoel Reach wrote:You, for example, are really me under an assumed name.

Thanks - I had suspected that, but it's good to be sure.

I always understood it to mean that you are expected to pay, and have to pay, just the court of law in this world cannot force you to pay