If I made a hole in the center of the moon I would experience zero gravity because all of the mass would surround me. Since a black hole is so named do we consider that the center also has zero gravity?
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A black hole is not a hole in a mass, like the hole you described in the moon. Rather, it is a mass collapsed at a singularity. Thus, at the center of the black hole, we would have to determine what happens at a singularity.
wheelix
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@weeeliam - and according to the information in the other answer and comment below the singularity is undefined for the Schwarzschild geometry but unformed in the physical case - thank you – FacingDownZ Jan 22 '20 at 12:37
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At the center of mass point, you are saying that you would experience zero gravity. What is correct to say is that you would feel weightless.
When r=0 the Christoffel symbol Γrtt is zero and that means the radial four-acceleration is zero and that means you're weightless.
Now your question for a Schwarzshield BH does not have an answer, because at r=0 the gravitational acceleration is undefined.
Anyhow, the point I'm gradually getting around to is that your question simply doesn't have an answer. This is because if you are asking about the idealised Schwarzschild black holes then the geometry is undefined at r=0 so the gravitational acceleration is undefined there. If you are asking about real black holes then the gravitational acceleration at the centre is finite because they haven't finished collapsing yet, and indeed won't finish collapsing at least until an infinite time has passed, or indeed not at all if they evaporate due to Hawking radiation first.
Árpád Szendrei
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Clarification about the weightlessness - thanks. I can see the main point in your answer is that the BH center is undefined so my question should get -1 – FacingDownZ Jan 21 '20 at 11:51
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@FacingDownZ I did not downvote. I like your question, I myself asked similar questions too. – Árpád Szendrei Jan 21 '20 at 22:01