Size and shape of a black hole singularity?

[kris kaczmarczyk]

How and if singularity is related to Plank size (h) , are they be related ? If they are; can the singularity have squared shape (like pixel) , if it is h size so that is the "smallest" understand by "physics" and any curve (circle) would break the rule of h begin the smallest ?
Does my question make any sense ?

 

[rootone]

'A singularity' just means a situation where math which usually works perfectly, like GR, is no longer producing sensible results, such as infinite density for a black hole singularity.
Questionable maths doesn't have a shape.

 

[PeterDonis]

How and if singularity is related to Plank size (h)

We don't know. According to classical GR, the singularity doesn't have a size. But we expect that quantum gravity will change what happens in a region of spacetime sufficiently close to the singularity. But we don't know how close is "sufficiently close" or what relationship that will have to Planck dimensions. The current best guess seems to be that Planck dimensions are roughly the scale at which quantum gravity effects will become significant, but we have no way of testing that any time soon.

can the singularity have squared shape

I don't think any quantum gravity speculations give a "shape" to the singularity.

 

[kris kaczmarczyk]

We don't know. According to classical GR, the singularity doesn't have a size. But we expect that quantum gravity will change what happens in a region of spacetime sufficiently close to the singularity. But we don't know how close is "sufficiently close" or what relationship that will have to Planck dimensions. The current best guess seems to be that Planck dimensions are roughly the scale at which quantum gravity effects will become significant, but we have no way of testing that any time soon.
I don't think any quantum gravity speculations give a "shape" to the singularity.

Thank you very much for your comments/answers! I have based my question on Hawking radiation, which as I understand derived from Quantum effects, so It make me think that if Event Horizon is govern by the Planck constant, why not the singularity? I am not a physicist, but great enthusiast, so please forgive/correct any mistakes.

I am just thinking about Cantor continuum and Plank length and how much can be fitted inside of it (3D Universe)?
Is it "legal" to think about physical objects (Plank length) in context of mathematics?

 

[PeterDonis]

I have based my question on Hawking radiation, which as I understand derived from Quantum effects

Yes, but only from an approximate theory of quantum effects, where everything but gravity is treated using quantum field theory, but spacetime/gravity is treated classically, using General Relativity.

if Event Horizon is govern by the Planck constant

It isn't. In the models that predict Hawking radiation, spacetime is classical. See above.

I am just thinking about Cantor continuum and Plank length and how much can be fitted inside of it

There are an infinite continuum of points inside a line segment one Planck length long, if we are using the continuum as our mathematical model. In fact, in the mathematical model, you can put any continuum of points into a one-to-one correspondence with any other--such as a Planck length's worth of points and a billion light-years' worth of points.

We don't know if this model still works under a full theory of quantum gravity because we don't have such a theory (yet).

 

[kris kaczmarczyk]

Thank you very much for your comments/answers! I have based my question on Hawking radiation, which as I understand derived from Quantum effects, so It make me think that if Event Horizon is govern by the Planck constant, why not the singularity? I am not a physicist, but great enthusiast, so please forgive/correct any mistakes.

I am just thinking about Cantor continuum and Plank length and how much can be fitted inside of it (3D Universe)?
Is it "legal" to think about physical objects (Plank length) in context of mathematics?

Or better yet -- good for the scifi book -- parallel universe which is shifted/offset for example by 1/2 Plank length ?

 

[PeterDonis]

parallel universe which is shifted/offset for example by 1/2 Plank length ?

Please review the PF rules on personal speculation.

 

[newjerseyrunner]

You should understand that even length is relative. A plank length while you're sitting here on Earth is not the same as a Plank length when you are traveling close to the speed of light.

Also, a square would be a terrible way to imagine a quantized spacetime. A square with edges of plank length 1, has a diagonal of 1.7 plank lengths.

The size and shape of any singularity is by definition: undefined. It'd be like if you have an equation 1 / (4 + x), what is the slope of the line at x = -4?

 

[kris kaczmarczyk]

thank you very much -- I am just speculating here, so any answer makes me happy
a) I guess for the local observer Plank length is Plank length, am I wrong?
b) I thought that there will be more objections to the corners (the surface is not smooth, my understanding is weak even in the sense of JR Weeks) , can you please elaborate more about why 1.7 is bad in this context?
c) I feel the same notions with the others answers, but that means that we apply mathematics (Platon objects) to the real word, I thought that if Plank length is the smallest physical reality then should the singularity stop there? That is why I am daring with this speculation. Also I like that Plank length was such a "simple" observation.

 

[PeterDonis]

for the local observer Plank length is Plank length

I'm not sure what you mean by "the local observer". In classical SR/GR, there is length contraction, and that doesn't change at the Planck scale; a Planck stick (one Planck length long in its rest frame) will look shorter than one Planck length to you if it is moving relative to you.

can you please elaborate more about why 1.7 is bad in this context

It's not just that 1.7 is bad. Thinking of "pixels of spacetime" of any definite shape is bad. We don't have a good theory of quantum gravity yet, but none of the options being pursued look anything like that.

if Plank length is the smallest physical reality

None of the quantum gravity options being pursued look anything like that either.

 

[kris kaczmarczyk]

Please review the PF rules on personal speculation.

I am sorry, what I was trying to ask is if it is possible that there maybe parallel Universe(s) "so close" less than Plank length? It is so far unreachable for us ; as you have mentioned before - energy level to observe it. Prof Saskind in War of Black Holes mentioned some experiments pointing to other Universes 5 millimeters away, if I recall correctly , but that was different dimension.

 

[PeterDonis]

what I was trying to ask is if it is possible that there maybe parallel Universe(s) "so close" less than Plank length?

This is personal speculation. It is out of bounds here.

 

[PeterDonis]

Prof Saskind in War of Black Holes mentioned some experiments pointing to other Universes 5 millimeters away

The Black Hole War is a pop science book, not a textbook or peer-reviewed paper.

There are peer-reviewed papers that talk about extra dimensions in the context of string theory, but that is not the same thing as "parallel universes".

 

[PeterDonis]

The OP question has been sufficiently addressed. Thread closed.