Today, as my teacher was lecturing us in calculus class about antiderivatives and definite integrals and such, he said something that made me think. There's no such thing as negative area. Common sense had me agreeing as he had said this times before, and graphically and logically it seems true. But then I thought about a black hole. Would those contain negative volume? Volume is a set amount of space, but from what I've learned, a black hole seems to bend that very law. They take up no space, right? But they can swallow entire planets and still leave no trace. Is this negative volume? Or is this just such extreme compression that overcomes atomic forces and just turns it into pure energy? I don't really know much about astrophysics like that, but I wanted to hear from the geniuses here instead of googling it or something. It's been bothering me all day.

 

I think the laws of physics and space-time doesn't apply in a black hole so it wouldn't be applicable to say volume

 

I thought at the middle of the black whole is a speck, which is the collasped star and everything else it has gathered. It keeps getting smaller as it compacts on itself but I think it is like an exponential equation, it gets VERY close to 0 volume but never actually reaches that point.

Just a thought

 

a Klein bottle comes close

I'd gather to say that in 3-D space-- no negative volume. but wait for Magician to chime in, as he's the resident mathematician.

 

tritium_pie: resident physic [sic]

A Klein bottle is a surface, not a volume.

As far as I know a black hole has a very tiny - but positive - volume, positive mass (duh!), and extremely high density.

Geometrically, volume is nonnegative. Whether this is an accurate model of the universe is impossible to say, but I, for one, wouldn't bet against it.

 

I'm not sure what you mean by "no trace". The mass of the swallowed planet is still there; I should think that qualifies as at least a trace.

 

That's correct, black holes do have volume. Geometrically area/volume is always positive. I know your prof probably told you that an integral is the area under a curve, and he's right - but it's a signed area, meaning it could be negative or positive.

 

from my (admittedly limited) understanding, a Klein bottle has zero volume.

(a quick Google search confirmed this: "Klein bottle no volume")

but... I am not a mathematician, and anybody can put up a website with less than accurate info, so I'll be the first to admit that I could be wrong.

 

Exactly. Anything that's a surface, has no volume. Think of a flat plane...

 

I think you worry too much about things you can't control. I wouldn't worry about it, unless of course you get swallowed up by a black hole.

Therapy session over, that'll be $100. Make the check out to WarrenW...

Warren