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There's the Talpiot Tomb
https://en.wikipedia.org/wiki/Talpiot_Tomb
It might not be him but also it might.
This conclusion, while weakly supported by a statistical analysis of the names involved, is rejected by most archaeologists, theologians, linguistic and biblical scholars.
There's a bunch of references for archaeologists debunking it.
I know you said "it might not be him" but I feel like that understates the weight of evidence against that possibility.
The respectable probability estimates range from astronomically unlikely to merely unlikely. In other words, we don't have incontrovertible ways of calculating the probability.
While it's not great or convincing evidence, it's the only physical evidence I know about.
We might not be able to calculate the probability but we can conclude that the chances that this tomb is that of Jesus is infinitesimal.
If you can't calculate the probability, then you can't rationally reach the conclusion that the probability is very low.
Of course you can.
I'm unable to calculate the probability that the moon will fall out of the sky tonight but I know that the probability is very low.
You can make the simple inductive calculation that the probability is 1 / (total number of nights moon didn't fall out of sky).
You can also look at the total energy needed to de-orbit the moon and come up with a frequencie for events at least of that magnitude.
They are easy calculations and they both give infinitesimal results. If that weren't true, there'd be no way to tell if your intuition were correct.
If you're happy with this type of calculation then the probability that this tomb is that of biblical Jesus is (number of occupants) / (number of humans in that area at the time the tomb was built).
That's way too low since several of the names match.
Enough. Feel free to continue believing that, on the balance of probabilities, this tomb is that of the really real Jesus.
After reading that page, I strongly suspect that's not him. It's all based on statistical modeling, and it's been heavily massaged. Even with that, they give it 1/600 odds (on the low end) of it being random chance, which those aren't bad odds.
Apparently the inscriptions are partially illegible, so assuming it's even correct their statistical model is based on the name Mariamne being Mary Magdelene (which is clearly not the name we remember her by) and being Jesus's wife, Maria being the mother, and Jesus having a son, which we didn't know about, named Judah, as well as a few other assumption that really do not feel like they should be making.
Even making a ton of assumptions, the odds are still not particularly convincing. It feels like something that can increase someone's faith if they don't question it, but if you examine it at all reveals how much people are reaching to prove what they already want to believe.
I'd have guess people who thought the tomb was for the Jesus would have their faith shaken by it since it would mean Jesus was married and had a kid, though there are some obscure Christian sects that have believed that.