Upper limit on the characteristics of Singularity

[surajt88]

"Upper limit" on the characteristics of "Singularity"

I know GR fails in "singularities". Is there an upper limit on characteristics of the singularity like a maximum value for the density of matter after which GR fails? I came across a number of threads which discuss what happens after something falls inside a supermassive black hole and it seems that GR holds well inside these objects within the event horizon. I would like to know the limits of GR, or in other words, at what point exactly does GR begin to fail in explaining the characteristics of matter that falls into the said supermassive black hole? Hope I made myself clear.

 

[bcrowell]

The only relevant scale is the Planck scale: http://en.wikipedia.org/wiki/Planck_length

Near a black hole, you can describe spacetime using GR as long as your distance from the singularity is roughly greater than the Planck length.

There is also a Planck mass, and therefore you can define a Planck density.

 

[surajt88]

Sorry for the layman questions, but does the plank length explanation imply that the size of the "singularity" is of dimensions comparable to the Planck length or is the dimensions of the singularity indeterminable by GR, but the characteristics of the infalling matter is determinable upto within Planck length of the singularity? Also, is the Planck length incorporated in GR to explain the limits of the theory?

 

[bcrowell]

Sorry for the layman questions, but does the plank length explanation imply that the size of the "singularity" is of dimensions comparable to the Planck length

I don't think we know, since we don't have a theory of quantum gravity.

or is the dimensions of the singularity indeterminable by GR,

That's certainly true.

but the characteristics of the infalling matter is determinable upto within Planck length of the singularity?

Not sure what you mean by this.

Also, is the Planck length incorporated in GR to explain the limits of the theory?

No, GR doesn't have Planck's constant in it, so it doesn't say anything about the Planck scale. If we didn't know about quantum mechanics, only GR, then we might suspect that something was going wrong when singularities were predicted, but we'd have no way of saying that there was a specific scale where GR broke down.

 

[surajt88]

Not sure what you mean by this .

I don't have a formal background in physics and so I'm having a hard time getting across with what I mean.

Near a black hole, you can describe spacetime using GR as long as your distance from the singularity is roughly greater than the Planck length.

The above post was what I wanted clarifications with. Let's assume an infalling observer measures the distance from the event horizon to within 1 Planck distance of the singularity using GR. From this distance and from his previous knowledge of the diameter of the (let's assume) non rotating black hole, wouldn't it be possible to calculate the "dimensions of the singularity"?
I know this would seem a stupid question but I am unable to find an answer to this.

 

[Nugatory]

Let's assume an infalling observer measures the distance from the event horizon to within 1 Planck distance of the singularity using GR. From this distance and from his previous knowledge of the diameter of the (let's assume) non rotating black hole, wouldn't it be possible to calculate the "dimensions of the singularity"?

The "singularity" is a point where the solution to the equations of general relativity makes no sense because it contains a division by zero. That doesn't tell us anything except that GR doesn't work at that point and that we need a different theory to describe what's happening in the neighborhood of that point.

Because it's a point, it also doesn't make much sense to talk about its dimensions.
However, I expect that what you're really asking is "Is there an upper limit on the size of the region where GR stops working?". Given that we don't exactly have a lot of observational data from inside an event horizon to confirm that GR works there, a fair case could be made that that's the upper bound. (not a very satisfying upper bound though, because we have every reason to expect that GR does work until we get much closer to the singularity).

The Planck length is a pretty convincing lower bound.

 

[surajt88]

The "singularity" is a point where the solution to the equations of general relativity makes no sense because it contains a division by zero. That doesn't tell us anything except that GR doesn't work at that point and that we need a different theory to describe what's happening in the neighborhood of that point.

Because it's a point, it also doesn't make much sense to talk about its dimensions.
However, I expect that what you're really asking is "Is there an upper limit on the size of the region where GR stops working?". Given that we don't exactly have a lot of observational data from inside an event horizon to confirm that GR works there, a fair case could be made that that's the upper bound. (not a very satisfying upper bound though, because we have every reason to expect that GR does work until we get much closer to the singularity).

The Planck length is a pretty convincing lower bound.

"Is there an upper limit on the size of the region where GR stops working?" was exactly what I meant. I read up a bit and realized that askin for the "dimensions of the singularity" in this case is akin to askin when infinity begins in an extended number line.

Does what you said above imply that GR fails in a spherical region of radius of about 1 Planck length at the centre of the black hole?