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I was watching the recent offering from BBC's Horizon - Who's Afraid of a Black Hole - and it got me thinking. It seems, as far as I can see, that far from Einstein's relativity not being able to explain the mathematics of a singularity, they explain it perfectly adequately. It seems, to me, that the scientists involved simply do not accept the idea of infinite density.Am I missing something here? In fact, on a very basic level isn't such a result absolutely obvious? If you are looking to discover the density of a measureless point in space which has mass, the result will clearly be infinite?

Quote from: angst on 07/11/2009 13:57:24I was watching the recent offering from BBC's Horizon - Who's Afraid of a Black Hole - and it got me thinking. It seems, as far as I can see, that far from Einstein's relativity not being able to explain the mathematics of a singularity, they explain it perfectly adequately. It seems, to me, that the scientists involved simply do not accept the idea of infinite density.Am I missing something here? In fact, on a very basic level isn't such a result absolutely obvious? If you are looking to discover the density of a measureless point in space which has mass, the result will clearly be infinite?The word "singularity" doesn't mean "point of infinite density" , though it is often taken to mean that (and popularly used to mean that). The word means a proposed state of a physical system where the mathematical description of the system does not make sense. For a singularity, we can derive a number of contradictory and non-sensical statements. Even in general relativity, there are singularities within the full description of a black hole. Some of them can be removed through a careful description of the objects, but not all of them. This is the real problem.

You need to be very careful when you start throwing infinities around, especially in the real world/universe.Density requires two factors; mass and volume, but the hypothetical singularities at the center of Black Holes have no volume, which isn't the same as infinitely small i.e. 0 ≠ 1/∞. Trying to apply the concept of density to the a singularity then, is not going to produce valid answers, and working on the basis that the density is infinite is really misleading yourself.The problem stems in part from the mathematical slight of hand that allows to to work with zero as a valid number. For example, lets say I want to give you a gift of an apple, so I give you zero apples, tell you to take one for yourself, and then ask you to give the remainder back to me. Mathematically, this is fine, but in real life it's nonsensical.With a BH, all we can say for sure is that space behaves as though there were a concentration of mass acting at that point, but not that there is a mass at that point. What we can almost certainly be sure of is that whatever is behaving as a mass at that point is not mass in any form that we know it and hence trying to apply density to it is equally invalid.