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Question: The tip of a crack in a continuum like glass is a singularity.

If we

A) set QM and Planck's volume arguments aside and stick to GR only

B) assume that at least some* blackholes contain a singularity and

C) assume black holes move in space-time,

then shouldn't it follow that the hole punctured in space-time due to the singularity is cutting/cracking/tearing space-time as it moves along?
Does the space-time get sewn back up magically?
Should it not leave a trail of damage behind?

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    In GR a singularity is completely unlike a crack in a solid medium. Any attempt to use one as a model for the other is doomed to failure. The best discussion of singularities I've seen is yess' answer to my question Interpretation of a singular metric. I recommend you read through that then reconsider your question. – John Rennie Nov 12 '15 at 19:29
  • You might be interested in this YouTube video of two black holes merging (the result of a computer simulation, mind you). – Kyle Kanos Nov 14 '15 at 11:55
  • Props for asking a question with interesting imagery, but because nobody knows exactly how a singularity behaves, it's impossible to say. Gravity bends space-time and black holes may even pull space with them as they rotate but I don't know how a "crack" in space-time is definable. – userLTK Nov 16 '15 at 08:38
  • Think of it like this, consider a big pan of water with a swirl (which in your case is the singularity) if the swirl moves the previous position is reformed –  Nov 16 '15 at 18:21

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You are thinking classical physics + General Relativity.

In the centre of a black hole is a gravitational singularity, a one-dimensional point which contains infinite mass in an infinitely small space, where gravity become infinite and space-time curves infinitely, and where the laws of physics as we know them cease to operate. As the eminent American physicist Kip Thorne describes it, it is "the point where all laws of physics break down".

In this sense, one can define the singularity as a trajectory in the space time reference frame of the earth, it is a moving point, but "crack" attributes characteristics to space time that it does not have. There are continuous distortions of space time due to the existence of the singularity and these have to be explored in the framework of General Relativity. It means that as t changes the functional forms in space of the distortions of the singularity change . There is no permanent space medium that would keep a record of the "passing" of the singularity. In the absence of mass/energy, space time is flat.

Current research is attempting to quantize gravity, which means that singularities become blurred, due to the uncertainties introduced by the probabilistic nature. Have a look at the current Big Bang model to get an idea of what happens to singularities when quantization of gravity is assumed.

anna v
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  • This is very missleading and incorrect. A singularity is not a point, nor a tragectory and is deffinitely not at a point with coordinates (x(t), y(t), z(t)). – MBN Nov 16 '15 at 09:01
  • @MBN a mathematical singularity at a point in space time in classical physics? note "classical" https://en.wikipedia.org/wiki/Singularity_%28mathematics%29 – anna v Nov 16 '15 at 09:14
  • @MBN Take a black hole in our universe, as we are moving and it is moving according to galactic forces, a trajectory exists, with time as a variable and changing space coordinates. A singularity is a point at the center of this black hole, classically. quantum mechanically it is a different story as I hint in my second paragraph – anna v Nov 16 '15 at 09:19
  • Yes, I am talking classically (i.e. non-quantum) as well. A singularity is nothing like what you describe. – MBN Nov 16 '15 at 09:44
  • @MBN can you give a link on what you say? – anna v Nov 16 '15 at 09:58
  • http://www.itp.uni-hannover.de/~giulini/papers/Geroch_Singularity_AnnPhys1968.pdf – MBN Nov 16 '15 at 10:43
  • @MBN not very satisfactory . from the abstract: "it is claimed that none of these definitions is satisfactory." I am sure theat the OP's question is not for deep navel gazing. Thanks for the reference, I will read it. – anna v Nov 16 '15 at 11:16
  • @MBN my answer is at this level http://www.physicsoftheuniverse.com/topics_blackholes_singularities.html , not at a research level of course – anna v Nov 16 '15 at 11:29
  • He is addressing those insatisfactory definitions and explaining what a singular space-time is. If you read the paper it should be satisfactory. – MBN Nov 16 '15 at 14:28
  • It doesn't matter what level your answer is aiming at, writing wrong and misleading things in you answer is not good and should be adited. – MBN Nov 16 '15 at 14:29