Originally Posted by cangus
Has anyone ever heard that the center of a black hole is a point in time rather than a place in space? If so, can someone please explain this to me? A Black hole in in physical reality (space) right? So, how is the center a point in time?
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Forget relativity for a moment, and think about the x-y-z coordinates for the physical 3-dimensional space. Fix z = 3 and let let x and y roam over all possible values. This corresponds to a 2-dimensional plane in space - the z = 3 slice.
Now move to the spacetime of special relativity, and consider an inertial reference frame. Set t = 3 and let x, y, and z roam over all possible values. A 3-dimension spacelike hyperplane results that represents, for the chosen reference frame, the single instant in time t = 0. On a standard spacetime diagram, this is represented as a horizontal line because the x and z spatial dimensions are suppressed.
Finally, consider Schwarzschild coordinates for the spacetime of an 'eternal" black hole. As pervect has already noted, inside the event horizon r is a timelike coordinate. A singularity "occurs" at the "centre" r = 0. Since r is a timelike coordinate, the singularity is spacelike. With 2 dimensions supressed, the (future branch of the) singularity r = 0 is represented on: a Kruskal-Szekeres diagram by a spacelike hyperbola; a Penrose diagram by a jagged horizontal line. Very roughly, these lines (actually hypersurfaces) correspond to the "instant in time" r = 0.
OF course, because of of its singular nature, r = 0 is not actually allowed as part of the spacetime manifold.
Regards,
George