When Black holes are getting formed, in which direction in space they form? For example, I have read that formation of Black Holes is same as forming a hole on a rubber sheet by a spherical ball, so it gets formed in a direction of the weight of the ball, so similarly if a star is going to be a black hole, in which direction of space will if form?
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I'm not sure a "direction" makes sense in this case. The rubber-sheet analogy is a poor visual image in this case. Why can't you just turn your view of the rubber sheet upside-down and say it forms up? I'm pretty sure the radius of the black hole as view from inside of the black hole is larger than the radius of the black hole as viewed from distance observer. In that case you could say space curves towards the center of the black hole (the singularity). – Brandon Enright Nov 14 '14 at 07:54
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I tink your question is mostly answered by the answers to the question Universe being flat and why we can't see or access the space "behind" our universe plane?.
The rubber sheet analogy gives the impression that there is an extra dimension in which spacetime is curved. Curvature in an extra dimension is called extrinsic curvature. However in general relativity no such extra dimension exists and the curvature is intrinsic curvature. So there is no 5th dimension direction in which spacetime is pulled to make the black hole.
John Rennie
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+1. We also use extrinsic curvature in GR; we treat the boundary of the spacetime as a submanifold, and its extrinsic curvature is part of the boundary term to properly define the stationary action principle. – JamalS Nov 14 '14 at 08:40
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@JamalS: Yes, OK, but the embedding in a higher dimension is a mathematical trick and not intended to represent anything physical. I feel this is a dangerous direction in which to lead beginners to GR :-) – John Rennie Nov 14 '14 at 08:42