Is the Curvature of Spacetime the Cause of Singularities in Black Holes?

[damgo]

Continuing on the PF2 thread about singularities... I had a thought that might give a sort of intuitive explanation of the singularity theorems -- eg the proofs that singularities exist at the center of black holes:

Remember how photons emitted just exactly at the edge of black hole are supposed to be 'trapped' there and not moving at all? Now, how do we reconcile this with the relativity notion of light always going at c? Well, in a frame right next to the edge of the black hole, you see the event horizon itself expanding at almost the speed of light -- run as you can, you can't escape it.

The intuitive picture this leads to is that the black hole is sort of "sucking" spacetime itself into it. The effect of curvature->pulling matter together->more curvature goes into a feedback loop, and the spacetime fabric pulls the matter into a singularity.

A better way to put it: in a black hole, the curvature of spacetime -- the rate at which distances shrink -- becomes greater than the speed of light. Since particles can't move faster than this, it doesn't matter what forces or accelerations they feel; spacetime 'wins' and keeps pushing them closer together.

From what I know of GR and have read of the singularity thms, this seems to be the intuitive/heuristic explanation of what the field equations actually say happens. I think... does this help anyone?

 

[chosenone]

If the gravitational field of a black hole,or singularity stretches spacetime doesn't mean that the distance between two points in the presents of gravity changes.one would think that the object traveling through spacetime always traveles the the same distance it should anyway,because before the object traveled near the black hole,spacetime was already stretched,so the distance should still be the same as it would anyway!

 

[RuroumiKenshin]

what about naked singularities? If they're real, then does that mean that there are singularities that are quite the contrary. So, what would happen if 2 singularities actually collided with each other?

 

[Hurkyl]

Is it true in general that all gravitating bodies "suck in" spacetime like that?

I have been trying on my own to figure out what black hole geometry looks like, and I had came close to the description you gave, but I conceptually blocked myself by thinking I needed to reconsile black hole geometry with the fact the event horizon occupies a static position in space-time by demanding that there was no "sucking" at the event-horizon, and was coming up with some odd conceptual ideas like space-time being continually warped more and more in an angular direction at the event horizon

Hurkyl

 

[damgo]

I think it's really only applicable to black holes... regular objects give a fixed curvature, no runaway effect. I suppose I should be saying "space" since spacetime doesn't change by definition.

> So, what would happen if 2 singularities actually collided with each other?
I have no idea...

 

[Hurkyl]

Hrm, oh, are different types of reference frames involved here? The classic schwartzchild solution for a static mass, of course, isn't flat... but an observer in his flat reference frame would see space being "sucked" towards the mass?

Hurkyl

 

[damgo]

Always does. :) The whole heuristic explanation was aimed at explaining (vaguely) what happens inside the horizon; I don't know how useful it would be outside. Coordinates of a particular observer there get so weird... I think it depends on what coordinates you want to use globally. Hmm.

 

[Mentat]

Originally posted by MajinVegeta
what about naked singularities? If they're real, then does that mean that there are singularities that are quite the contrary. So, what would happen if 2 singularities actually collided with each other?

"Naked singularities"?

 

[damgo]

Whereas Stephen W. Hawking firmly believes that naked singularities are an anathema and should be prohibited by the laws of classical physics,
And whereas John Preskill and Kip Thorne regard naked singularities as quantum gravitational objects that might exist unclothed by horizons, for all the Universe to see,

Therefore Hawking offers and Preskill/Thorne accept, a wager with odds of 100 pounds stirling to 50 pounds stirling, that

When any form of classical matter or field that is incapable of becoming singular in flat spacetime is coupled to general relativity via the classical Einstein equations, the result can never be a naked singularity.

The loser will reward the winner with clothing to cover the winner's nakedness. The clothing is to be embroidered with a suitable concessionary message.

Stephen W. Hawking, John P. Preskill, Kip S. Thorne
Pasadena, California, 24 September 1991

Conceded on a technicality by Stephen W. Hawking, 5 February 1997

http://www.theory.caltech.edu/people/preskill/old_naked_bet.html

 

[RuroumiKenshin]

Originally posted by MajinVegeta
what about naked singularities? If they're real, then does that mean that there are singularities that are quite the contrary. So, what would happen if 2 singularities actually collided with each other?

Note that the revolving singularities can't be naked singularities!

 

[marcus]

Originally posted by damgo
Continuing on the PF2 thread about singularities... I had a thought that might give a sort of intuitive explanation of the singularity theorems -- eg the proofs that singularities exist at the center of black holes:

Remember how photons emitted just exactly at the edge of black hole are supposed to be 'trapped' there and not moving at all? Now, how do we reconcile this with the relativity notion of light always going at c? Well, in a frame right next to the edge of the black hole, you see the event horizon itself expanding at almost the speed of light -- run as you can, you can't escape it.

The intuitive picture this leads to is that the black hole is sort of "sucking" spacetime itself into it. The effect of curvature->pulling matter together->more curvature goes into a feedback loop, and the spacetime fabric pulls the matter into a singularity.

A better way to put it: in a black hole, the curvature of spacetime -- the rate at which distances shrink -- becomes greater than the speed of light. Since particles can't move faster than this, it doesn't matter what forces or accelerations they feel; spacetime 'wins' and keeps pushing them closer together.

From what I know of GR and have read of the singularity thms, this seems to be the intuitive/heuristic explanation of what the field equations actually say happens. I think... does this help anyone?

This is an intriguing thread and it would be great to see more of these. I would be glad if PF mentors would start threads on interesting subjects----often!


In the Astronomy game chroot just calculated that a 1.5 trillion solar mass hole (of the usual sort) would have surface gravity of one standard Earth gee. 9.8 meters/second^2.

I am wondering what it would be like to be lowered on a long strong cable down to near (but not touching) the event horizon and experience that normal gee gravity. Must go but maybe be back later

 

[marcus]

Originally posted by marcus
This is an intriguing thread and it would be great to see more of these. I would be glad if PF mentors would start threads on interesting subjects----often!


In the Astronomy game chroot just calculated that a 1.5 trillion solar mass hole (of the usual sort) would have surface gravity of one standard Earth gee. 9.8 meters/second^2.

I am wondering what it would be like to be lowered on a long strong cable down to near (but not touching) the event horizon and experience that normal gee gravity. Must go but maybe be back later

For starters the event horizon would look very flat to me because the radius of a 1.5 trillion solarmass hole horizon is 3 trillion miles.

So I would be being lowered down to near the surface of a very large ball----3 trillion mile radius ball. And it would look like a flat plane stretching to infinity.

Light rays are not bent very much in one Earth gee so optically things would not be too surprising for ME

The people in the Starship Enterprise up there who lowered me by the cable and who are watching me might see a lot of weird effects. Like I would be moving around and waving signs at them very slowly and I would be redshifted and all that.

We have a long cable so they are way higher in gravitational potential than me so there are all those effects. But for me in my own neighboring space down near the surface I don't think it would be too strange.

Only that, looking up, I would see the Ship and much of the usual starry panoply of heaven concentrated in a patch of sky directly overhead, and blueshifted, instread of being spread out as per normal. A kind of "fish-eye optics". I could probably see the stars on the other side of the black hole--with their light bent around so as to be in my periferal vision. So that's weird. But right around me probably would seem OK.

Anyway I don't picture the event horizon rushing at me at the speed of light---as per damgo's picture of what it would be like to be near the event horizon. So this is a difference of viewpoint which is interesting.

Damgo what do you say to this example and could you resolve the difference or say where the mistake is if any?

 

[LogicalAtheist]

What's a singularity?

 

[marcus]

Originally posted by LogicalAtheist
What's a singularity?

Hello Atheist, I was first in line and my question was about this
thing damgo said:

"...light always going at c? Well, in a frame right next to the edge of the black hole, you see the event horizon itself expanding at almost the speed of light -- run as you can, you can't escape it."

the singularity is way far away down in the center of this 3 trillion mile radius sphere. We are close to the surface---not actually touching it but close.

do you think we see the surface rushing at us at the speed of light?

What is it like, in your view, anything to report? You help me imagine the surface and I promise to help you imagine what if the string broke and you fell thru and ended up at the singularity

 

[LogicalAtheist]

Still confused. I'll have to read books on the subject.

What books would you guys recommend on reading about theses areas of physics?

I am interested in studying especially cosomoligical areas of physics, and strange things like relativity and light...

Currenty I'm reading THE ELEGANT UNIVERSE

Lemme know so I can learn please...

 

[marcus]

Originally posted by LogicalAtheist
Still confused. I'll have to read books on the subject.

What books would you guys recommend on reading about theses areas of physics?

I am interested in studying especially cosomoligical areas of physics, and strange things like relativity and light...

Currenty I'm reading THE ELEGANT UNIVERSE

Lemme know so I can learn please...

I remember you from "current radius of the observable universe" thread. You said:

"Marcus - It's unfortunate no one here was able to give you the answer to your question "what is the current radius of the universe".

The answer is: 4 x 10^26 meters

There you have it."

And that's right! I converted it to light years and it came out to 42 billion LY, about three times the Hubble distance.

So you have some grasp of cosmology. The Elegant U is supposed to be an excellent book---one could read it at whatver level I imagine. Havent read it myself. If someone else shows up they may have suggestions.

I would go directly to journal articles even if they are dense and often frustrating. I am leery of popularization. I read journal articles and do thought experiments.

I know some journal articles in arXiv that are kind of accessible if you decide you want to go that route.

Michael Turner has an outstanding summary of the changes that have occurred in cosmology in the last 5 years and where the field seems to be going. But it is written in dense academic style (with some formulas) so you have to really want to read it.

The web is a great place, with Ned Wright's cosmology tutorial and movies of what you see falling into a black hole and all those goodies. The web is almost better than books---if its for cosmology.

Keep me posted on your progress. I like cosmology.

 

[LogicalAtheist]

marcus - Wow you actually referenced me knowing a piece of information! How cool!

You know, the article I got that from stated that that actual size was called a Hubble volume, meaning whatever the size of our universe is is the current "hubble volume".

So what's with that? Is there double usage here?

 

[marcus]

Originally posted by LogicalAtheist
marcus - Wow you actually referenced me knowing a piece of information! How cool!

You know, the article I got that from stated that that actual size was called a Hubble volume, meaning whatever the size of our universe is is the current "hubble volume".

So what's with that? Is there double usage here?

there seems to be a double usage, unfortunately.

1.the Hubble time t_Hubble is 1/H₀

that's for sure, at least no confusion there. and it is not equal to the age exactly (what the age is depends on various things, but no matter what the age is, t_Hubble is always t_Hubble , a definite independently defined interval of time.

2. the Hubble length is just c t_Hubble
the distance light can travel in that interval of time.

As for the rest, confusion apparently

In Scientific American and popularized cosmology, where one can be somewhat vague and needs to have concepts immediately mean something to the reader-----one says Hubble volume is
"the volume of the observable universe" or something.
But I do not see that in scientific journals. On the contrary there was a large computer simulation project called "Hubble volume
project" where the volume of space simulated was a cube
one c t_Hubble on a side. I double checked this and it was clear.

The volume of the so-far observed universe is not that cube but a spherical volume and quite substantially larger----many Hubble volumes worth.

So the difference between the professional cosmologist language and the Scientific American popular style is immediately apparent right there.

So in answer, yes there seems to be split usage---that is a bit confusing and I can't say how this will be worked out. I suppose eventually it will be made consistent, maybe by people adopting an entirely new word or somehow else.

thank goodness Planck length, area and volume are unambiguous

 

[maximus]

i have always thought that (not including naked singularities) the area of the event horizon increase to a maximum, as does the entropy of the universe. an icrease in area greater than c would suggest an increase in entropy thus.

 

[LURCH]

Originally posted by marcus

In the Astronomy game chroot just calculated that a 1.5 trillion solar mass hole (of the usual sort) would have surface gravity of one standard Earth gee. 9.8 meters/second^2.

How?! At the EH, escape volocity is > c. At 1G, escape volocity is much less than c. The very definition of the Event Horizon is the distance at which gravitational influence becomes so strong that light cannot escape. Wouldn't that have to be the same G-force, regardless of the mass of the BH?

 

[Janus]

Originally posted by LURCH
How?! At the EH, escape volocity is > c. At 1G, escape volocity is much less than c. The very definition of the Event Horizon is the distance at which gravitational influence becomes so strong that light cannot escape. Wouldn't that have to be the same G-force, regardless of the mass of the BH?

Surface acceleration Where (9.8 m/sec²) = 1g

A= GM/r²

Escape velocity,

V=[squ]( 2GM/r)

Radius of event horizon:

c = [squ](2GM/r) solved for r

r= 2GM/c²

substitute 2GM/c² for r in the first equation:

A= GM/(2GM/c²)²

A = c⁴/4GM

assign A=9.8 m/sec

9.8 = c⁴/4GM

solve for M

M = c⁴/39.2G

Remember, g is a measure of acceleration while escape velocity is a velocity. They do not go up necessarily hand in hand. For instance the Surface g of Uranus is less that that of Earth's but the escape velocity from the surface is greater.

A lot has to do with the density of the Body (Uranus has a lesser density than Earth's)

Go back and look at the formula for the radius of a Black hole. Note that the radius is directly porportional to the mass. (double the mass, double the radius.) But the volume increases by the cube of the radius. Therefore, if You double the mass, you double the radius and increase the volume by a factor of 8 , since density is mass/volume, you've decreased the density by a factor of 4.

 

[marcus]

Hello Lurch,
I said:
[In the Astronomy game chroot just calculated that a 1.5 trillion solar mass hole (of the usual sort) would have surface gravity of one standard Earth gee. 9.8 meters/second^2.]

And then you said:

Originally posted by LURCH
How?! At the EH, escape volocity is > c. At 1G, escape volocity is much less than c. The very definition of the Event Horizon is the distance at which gravitational influence becomes so strong that light cannot escape. Wouldn't that have to be the same G-force, regardless of the mass of the BH?

Did you look back to the Astronomy game thread and see how he calculated it? It was correct. You could ask him----write a PM (personal message). Chroot knew what he was doing and you could learn something by asking him how he did it.

I know how I would calculate it but you might not like my way.
For an uncharged non-rotating BH the standard formula for the g at the EH is simply 1/4M, in natural units.
Earth g = 1.76E-51
So I just need to solve the equation
g = 1/4M

M = 1/4g = 1/(7E-51) = (1/7)E51

The mass of the sun is about E38, so this is about
(1/7)E13 solar masses-------1.5 trillion solar masses if done with care.

Chroot worked it out in metric units and got it right.

There is no rule that says gravity has to be particularly strong at the EH of a BH. It just has to be strong enough that light can't escape from it. One Earth gee is enough it it extends at about that same strength for billions of miles straight up. Even light can get discouraged and fall back.

 

[marcus]

Oh I see Janus stepped in while I was thinking what to say.

Glad to get some help! If I had known you were responding to Lurch I would have not replied.

I see we both used the same formula, you said

g = 9.8 = c⁴/4GM

And I was using natural units so c and G did not appear and said

g = 1/4M

I suspect Chroot used the same algebra that Janus just did