B Why Don't We Live Inside a Black Hole?

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We know the Big Bang Theory states that our universe was started from a hot-dense point. But should't it became black hole and every matter and radiation pulled to singularity? We would not be her if that is the case.
 
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Narasoma said:
We know the Big Bang Theory states that our universe was started from a hot-dense point.
It is unfortunate that you "know" that, since it's not true.

The "Big Bang Theory" doesn't actually say anything about how the universe started. That is, that theory does not posit a creation event. It posits a starting universe in a hot dense state, which may have been infinite in extent or may have been finite, but if finite, it was not a single point in space. That plasma state evolved into the universe we live in today.
Narasoma said:
But should't it became black hole and every matter and radiation pulled to singularity? We would not be her if that is the case.
I suggest a forum search. the question has been answered here dozens of times as to why we don't live in a black hole.
 
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Narasoma said:
But should't it became black hole and every matter and radiation pulled to singularity?
A black hole is a vacuum spacetime. The Big Bang is based on a spacetime with matter everywhere. They are not equivalent.
 
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Narasoma said:
should't it became black hole and every matter and radiation pulled to singularity?
No. The matter and radiation in the early universe was expanding very rapidly. Far too rapidly for any of it to collapse to a black hole, even at the very high densities of the early universe.
 
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From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
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