# Points in space and black holes

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## Main Question or Discussion Point

Well I read that points in space are indeed finite and intuitively they have to be because I guess we'd never be able to move from one point to the other. (intuitively this make sense)

However, when a black hole is created it is said a singularity is formed i.e. and infinitesimal point in which all mass is pulled towards by the immense gravity.

These two points are indeed paradoxical in nature because if points are finite then how can an infenitesimal point be created. There would have to be a rip in the fabric of space and time itself as we know it and I'm guessing that would have some weird effects.

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The reason its called a singularity is cause we don't really have any idea how stuff works in there... There are lots of reasons why a,b and c don't really make sense at that point - and there are lots of theories trying to explain / fix the myriad problems and questions with black holes.

Just by semantics, a "point in space" really needs to be finite. I think, ironically, that the best way to define finite is not-infinite. Infinitesimal is quite finite then! Maybe you're saying that a point in space must be finite and non-zero? There are many theories that suggest that space is discrete, and quantified - i.e. you cannot have an infinitesimal or arbitrarily small region of space -> but i think the general belief is that you actually can. In which case there wouldn't be a contradiction.

In the theories that call for quantized space(-time), to my knowledge black-holes also would be of finite, non-zero size. In string theory, the "singularity" of a black-hole does have a size, its not an infinitely small point -> so again, in that theory, there is no contradiction.

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Hmm interesting observations thanks.

anyone else with other thoughts?

These two points are indeed paradoxical in nature because if points are finite then how can an infenitesimal point be created.
I also believe that is quite the weird idea, however, since we cannot say what exactly is happening at that point, it still may be finite. There are many theories that say the singularity could be finite as the guy above me stated.

stevebd1
Gold Member
There seems to be a theory that a 'singularity' might consist of Planck matter (Planck density is 5.155x10^96 kg/m^3 which would result in matter becoming infinitesimally small (relative to human scale), the entire universe could fit into a volume the size of a proton based on this density). From what I can gather, the energy that makes up both matter and space combines at Planck dimensions, creating a quantum 'foam' supported by either Loop Quantum Gravity or strings. Though it has dimensions, this might technically still be described as a singularity as it is a combination of both matter and space (and probably time) rather than just collapsed matter in space. You have neutron stars, quark stars and the hypothetical preon star, you might argue that black holes are Planck stars, very compact stars that simply have an escape velocity that exceeds the speed of light.

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The singularity of a black hole is not a point in space it is not even a point in spacetime, in fact it is not even in spacetime.

stevebd1
Gold Member
The singularity of a black hole is not a point in space it is not even a point in spacetime, in fact it is not even in spacetime.
While it's all theory as to what goes on inside a black hole, isn't there a prediction that the coordinate intervals become space-like inside the black hole ($c^{2}\Delta t^{2}<r^{2}$) so that while it's not spacetime that we recognise (time-like) it's still a form of spacetime. So while the 'singularity' might not necessarily be sharing the same portion of space (or time) as the universe outside the event horizon, it is somewhere spinning and exerting gravity, pulling what ever falls past the event horizon towards it.

If there are implications of time becoming ambiguous inside a black hole then I imagine the same might apply inside the ergoregion of a rotating black hole where coordinates have space-like intervals also.

From everything that I've read, nothing ever reaches the center of a black hole from the view of an outside observer. As an object approaches the event horizon, the gravitational red shift increases, eventually shifting to an infinite red shift at the horizon itself.

According to that it would take an infinite amount of time for an object to reach the center of the hole, at which point the black hole itself would have had enough time to totally evaporate? I'm no expert, but if my logic is sound it would seem that there never is a point problem because time dilation occurs to a large enough degree that anything past the event horizon is evaporated out before it can get to the center.