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Are black holes explained by complex analysis? 
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#1
Apr813, 08:11 PM

P: 330

Is the center of a black hole essentially a pole, or a "point at infinity"? I always thought about this in my complex analysis class because one variable complex functions are 4 dimensional, which could translate into spacetime. Black holes have to have infinite density in their center, too, right? And the extremely strong gravitational field would basically make time go to zero?



#2
Apr813, 08:45 PM

Sci Advisor
P: 734

Infinities simply do not work in math, and a zerosize point of any mass would require infinite mass, which we know is not the case since black hole masses can be measured and are definitely not infinite. The "old" zeropoint/infinite mass "singularity" definition has been dropped as far as I have read recently. 


#3
Apr813, 08:47 PM

P: 330

So does time practically stop at the center of a black hole because of the immense gravitational field?



#4
Apr813, 09:19 PM

Sci Advisor
P: 734

Are black holes explained by complex analysis?
Inside the BH, time would seem to continue for any observer who might survive. Most PF posters are aware (I think) that an observer (human?) could survive inside the EH if the BH was large enough so that the gravitational pull at the EH was not strong enough to cause the "spaghetti effect". Near a small BH, the "spaghetti effect" would tear any matter apart, even individual atoms, before the EH was reached. 


#5
Apr1113, 06:22 AM

P: 534




#6
Apr1113, 06:40 AM

P: 534




#7
Apr1113, 06:48 AM

P: 534

Having said that, of course we don't really know what happens at (and very close to) the singularity since general relativity should get corrections in that regime.



#8
Apr1113, 07:13 AM

PF Gold
P: 6,093

I don't get that either. It does imply infinite DENSITY, but how do you get that it implies infinite mass? 


#9
Apr1113, 10:00 AM

Sci Advisor
P: 734

The gravity of the large mass still exists and the measure of the mass determines the EH boundry, but the mass (or density) is not infinite. 


#10
Apr1113, 10:21 AM

Sci Advisor
P: 734

p=m/V. 


#11
Apr1113, 11:40 AM

P: 5,632

GR and QM breakdown in the vicinity of the singularity....In any case, as you approach such a 'point', quantum foam seems to blur space, time, mass etc....We just do not yet have a theory that works in those conditions. 


#12
Apr1113, 12:04 PM

PF Gold
P: 6,093

This seems to tie in with your being wrong about infinities not working in math, which they do. Do you not get that 3/0 = infinity? 


#13
Apr1113, 01:42 PM

Sci Advisor
P: 734

Black Holes are physical entities with only 4 "detectible" properties, as opposed to Wheeler's original 3 "nohair" properties. I have (long ago) posted at least 34 separate posts regarding the four properties, yet still today books, and PF posts, ignore that. And the gravity of a BH is proportional to its finite mass. If we have to use any infinities to describe any properties of a BH, then all that can be said is that "we don't know". (I saw that on TV) 


#14
Apr1113, 04:42 PM

P: 907

The way you deduce infinite density is by assuming zero volume and a finite mass. If you accept the conclusion of infinite density but then reject the assumption of zero volume in favor of a different assumption of nonzero volume, you are committing an error. You can't have your cake and eat it too. A real mathematician would probably say that a finite mass divided by a zero volume is undefined rather than infinite. Or he would admit that he's not working in the field of real numbers but rather in some compactification thereof. A physicist is not bound by those rules. But he is bound to not call the volume zero in one breath and nonzero in the next. 


#15
Apr1113, 05:09 PM

Sci Advisor
P: 734

I think that we generally agree but have a "semantics" problem going on here. 


#16
Apr1113, 07:52 PM

P: 907

That you accepted it for purposes of a reductio ad absurdum is irrelevant. You are not allowed to have it both ways in the same argument. 


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