How Do Black Holes Form from Space-Time Curvature?

Gravitonion
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If gravity is a distortion between space and time, then how come black holes are formed, only the surface of an object should then exert gravity, right?
 
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In general relativity, gravity is represented as curvature in space-time. Space-time exists everywhere, even inside solids. Every atom has its own gravitational field, it's own little dimple in space-time, and they all add-up to make the object's gravity. Black holes are formed when enough little bits gather together so that the escape velocity some distance from the objects center of mass is greater than the speed of light.
 

Thread 'Euclidean geometry and gravity'

I asked a question here, probably over 15 years ago on entanglement and I appreciated the thoughtful answers I received back then. The intervening years haven't made me any more knowledgeable in physics, so forgive my naïveté ! If a have a piece of paper in an area of high gravity, lets say near a black hole, and I draw a triangle on this paper and 'measure' the angles of the triangle, will they add to 180 degrees? How about if I'm looking at this paper outside of the (reasonable)...
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Thread 'Is the variation of the metric ##\delta g_{\mu\nu}## a tensor?'

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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