What is the difference between an event horizon and a singularity?

tommac · #1 (**permalink**) 26-June-2008, 03:09 PM

Sorry about the newbie question but after a bunch of thought they seem like the same thing.

Chris Hillman · #2 (**permalink**) 26-June-2008, 03:15 PM

A very nice survey paper which

is very readable,
was written by an expert on black holes
is available for free download by anyone
should be a standard citation in discussion forums like BAUT

is:
Jean-Pierre Luminet
Black Holes : A General Introduction
in Black Holes : Theory and Observation,
F. Hehl, C. Kiefer, R. Metzler, editors.
Springer, 1998

See http://www.bautforum.com/about-baut/...-q-sticky.html for my suggestions for a new Q&A sticky.

HTH; I'll let someone else (publius?) take it from here!

tommac · #3 (**permalink**) 26-June-2008, 03:29 PM

Quote:

Originally Posted by Chris Hillman

The OP needs to clarify whether he means "coordinate singularity" or "curvature singularity", since the event horizon can be considered an example of one of these :wink: Also, just one is a coordinate-free concept, and ...

I'll let someone else (publius?) take it from there.

Well maybe we can start with the difference of those two. Maybe the answer lies in there. Basically what confuses me is the following. Please jump in when I assume something I shouldnt.

1) Closer to the event horizon the slower time runs relative to us. This then should mean that space is also compacted relative to our space.

2) At the EH. Time stops relative to us. Also Space compacts infinitely.

Isnt that basically the definition of a singularity?

tommac · #4 (**permalink**) 26-June-2008, 04:01 PM

OK ... during coffee I think I get a little of your singularity posts above.

an event horizon is a coordinate singularity ...
A BHs singularity is a curvature singularity as it is represented the center point of the curvature.

However I may disagree ...that an EH isnt both.

sabianq · #5 (**permalink**) 26-June-2008, 05:23 PM

By definition an Event Horizon is just a boundary beyond which events cannot affect or be observed by an outside observer.

you can think of the drain in your shower of an event horizon, you cant observe the water after it swirls down the drain.

a gravitational singularity is a place where spacetime folds in on itself as gravitational force becomes infinite.

I think i am wrong here ^^^^
I no longer think the gravitational force becomes infinite, more like as the mass of an object becomes so dense, the gravitational distortion becomes steeper, its "steepness" or how fast falling bodies "fall"into the gravity well, is a function of mass. as you add more mass, the "steeper" spacetime gets. and when you keep adding mass, eventually it the object reaches a point where it has such an effect on space time that that "steepness" is causing objects to fall into with a terminal velocity equal to the speed of light. we know mass cant go at the speed of light so it changes form into energy as it falls toward the event horizon.

tommac · #6 (**permalink**) 26-June-2008, 05:49 PM

Quote:

Originally Posted by sabianq

By definition an Event Horizon is just a boundary beyond which events cannot affect or be observed by an outside observer.

you can think of the drain in your shower of an event horizon, you cant observe the water after it swirls down the drain.

a gravitational singularity is a place where spacetime folds in on itself as gravitational force becomes infinite.

But what is gravitational force without space-time?
Neither time nor space can exist relative to us at the EH or beyond. So what is the distance to the singularity? For things falling in how long would they take to travel a mile in the direction of the singularity?

Am I wrong about assuming that time stops at the EH? wouldnt that mean that space is infinitely compressed? Wouldnt that mean that events can not happen even at the event horizon ... nor could anything pass beyond the EH .. but rather get stuck on the EH as time and space stops.

tommac · #7 (**permalink**) 26-June-2008, 06:12 PM

Take figure 4 of the link that Chris kindly provided above. It seems to show the collapse of star. However if time stops relative to us when the star collapses to the size of the event horizon. Then t does not progress any further ( relative to us ). Neither can the star collapse further because space-time itself is infinitely compressed.

So a star should not be able to collapse to a smaller size than the point where

Quote:

GM/R, exceeds
the square of the speed of light, c2.

Any further collapse would need to happen in imaginary space-time ( relative to us ).

As time has stopped.

Tim Thompson · #8 (**permalink**) 26-June-2008, 06:25 PM

Quote:

Originally Posted by tommac

Am I wrong about assuming that time stops at the EH?

Yes. Time does not stop at the event horizon.

A singularity is a point or locus of points where the singular quantity, whatever it may be, is undefined. The singularity that happens at the event horizon is called a coordinate singularity because it disappears if you change coordinate systems. Time appears to stop at the event horizon, relative to a distant observer. If I am here looking at the event horizon over there, I will say that I see time stopping over there. But if I carry a clock with me and fall through the event horizon, I will not notice any peculiar behavior of the clock, time will not slow or change. So the "stopping" of time is only an appearance which depends on my choice of time coordinates. So the event horizon is a singularity, but it is one we can gwet rid of in simple fashion, and one that depends on who is looking at it and how they are looking at it.

On the other hand, the singularity at the center of the black hole (a point for a Schwarzschild non-rotating black hole, a circle for a rotating Kerr-Newman black hole) does not depend on the observer. All observers will report a singularity. All coordinate systems are singular. The singular quantities, whatever they may be, will remain singular regardless of coordinate transformations.

So for the latter kind of singularity the theory, in this case general relativity, is always incapable of describing what happens, and is always undefined at the singular point(s).

tommac · #9 (**permalink**) 26-June-2008, 07:22 PM

Quote:

Originally Posted by Tim Thompson

Yes. Time does not stop at the event horizon.

Time appears to stop at the event horizon, relative to a distant observer. If I am here looking at the event horizon over there, I will say that I see time stopping over there. But if I carry a clock with me and fall through the event horizon, I will not notice any peculiar behavior of the clock, time will not slow or change. So the "stopping" of time is only an appearance which depends on my choice of time coordinates.

I am clear that I am stating that time stops relative to us ( we are a distant observer). I realize that entering the EH you still have time. But lets forget about the local case for now.

Lets look at this just from the distant observer. Time stops. If time stops and space is infinitely compacted. Then the star can not collapse further ( from our perspective ). TIme is stopped ... space is compressed ( to a plane-like sphere of 0 ( or close to 0 ) thickness ... that takes up a voume of space ???

Nothing more can progress ... only in infinite time. So if we see a black hole from a collapsed star wouldnt we only be seeing the star at the point of its collapse when it was the exact size of the event horizon?

That is my main point ... If you want we can talk about locally but as in Chris's article ... it is really more like the butterfly and the candle.

My imagination would say that passing the event horizon would show a singularity. I think the singularity would be infinitely far away and we would sense us being pulled at the speed of light towards it.

tommac · #10 (**permalink**) 26-June-2008, 07:49 PM

Quote:

Originally Posted by Tim Thompson

On the other hand, the singularity at the center of the black hole (a point for a Schwarzschild non-rotating black hole, a circle for a rotating Kerr-Newman black hole) does not depend on the observer. All observers will report a singularity. All coordinate systems are singular. The singular quantities, whatever they may be, will remain singular regardless of coordinate transformations.

Then ... the only thing I can derive from this is that from a distance the singularity as you describe here is both the singularity and the EH (from our perspective ). The pure singularity created from a fully collapsed star could never have been created. I guess it would only get created as you moved close enough ( to get gobbled up ) where the EH time would move relative to you.

Disinfo Agent · #11 (**permalink**) 27-June-2008, 09:44 PM

Quote:

Originally Posted by tommac

Lets look at this just from the distant observer. Time stops. If time stops and space is infinitely compacted. Then the star can not collapse further ( from our perspective ). TIme is stopped ... space is compressed ( to a plane-like sphere of 0 ( or close to 0 ) thickness ... that takes up a voume of space ???

Nothing more can progress ... only in infinite time. So if we see a black hole from a collapsed star wouldnt we only be seeing the star at the point of its collapse when it was the exact size of the event horizon?

Yes.

tommac · #12 (**permalink**) 27-June-2008, 10:49 PM

Quote:

Originally Posted by Disinfo Agent

Yes.

OK then at this point in time ... No stars have collapsed beyond the point of the EH.

Argos · #13 (**permalink**) 27-June-2008, 11:46 PM

Quote:

Originally Posted by tommac

So what is the distance to the singularity?

It is the critical radius. The singularity is at the center of mass of the collapsed star.

Quote:

For things falling in how long would they take to travel a mile in the direction of the singularity?

The time as measured by your clock, which is not affected.

Tim Thompson · #14 (**permalink**) 28-June-2008, 06:55 AM

Quote:

Originally Posted by tommac

Lets look at this just from the distant observer. Time stops.

Actually, no it doesn't. The whole point of the "coordinate singularity" is that it is only an illusion. Despite the title "relativity" we must remember that events are absolute. Everything that happens in one reference frame happens in all reference frames. If one observer sees something blow up, all observers will see it blow up. If two things smash into each other in one reference frame, they will smash into each other in all reference frames. And if something falls into the black hole in one reference frame, it will fall into the black hole in all reference frames. It only "looks like" things don't fall in, it only "looks like" time stops, but it is no more correct to say that time actually stops than it is to say that an optical illusion is real because we can see it. What we "see" is not reality, what really happens is reality.

sabianq · #15 (**permalink**) 28-June-2008, 07:17 AM

Quote:

Originally Posted by tommac

But what is gravitational force without space-time?
Neither time nor space can exist relative to us at the EH or beyond. So what is the distance to the singularity? For things falling in how long would they take to travel a mile in the direction of the singularity?

Am I wrong about assuming that time stops at the EH? wouldnt that mean that space is infinitely compressed? Wouldnt that mean that events can not happen even at the event horizon ... nor could anything pass beyond the EH .. but rather get stuck on the EH as time and space stops.

hi there
please someone let me know if i am off base here.

first, you must understand that energy and mass are the same. they are synonymous with each other and if you are describing one form like mass, you are in fact describing the other form energy and vice versa.

from what I understand, gravity is a construct of the geometry of spacetime, energy warps this spacetime. if you get enough energy together in one spot, you can literally deform spacetime, and i would guess that the amount of "warpage" is directly proportional to the amount of energy you have in one spot.

so if you have no energy, then spacetime would be flat. and i think that there is evidence that space time is indeed flat when there is no gravitational influence.

what really needs to be inserted here is a definition of what spacetime is.
is it a fabric? is it an aether?
it is funny that the same mathematical laws that describe prorogation and reflection of an acoustic wave also apply to electromagnetic radiation.
it seem to me that if the same math applies, and sound is transmitted through a medium, then i would have to conclude that spacetime is infact a medium of some sort. I would show this logically by suggesting that spacetime has to be something fundamental to this universe, maybe the "surface" of a higher dimension or something.
Regardless, light propagates through spacetime, which can be affected, distorted or warped by mass (which is ironically, Energy).
we can see this warp by observing the path of light say with the use of a gravitational lens.

I would even suggest that it is a misnomer to say that gravity "pulls" you
rather an object is in free fall what it enters a gravity field.

If you can get enough energy in one spot, You can have a situation where the warpage of space time becomes so steep that anythig falling into its gravitational field will fall at a speed of equal to c.

the event horizon of a black hole is only a boundary where the speed of fall toward a gravitational "well" becomes equal to the speed of light. the steepness of the gravity well could be measured in how fast something "falls" toward it. "remember in a vacum , a feather and a hammer fall at the same speed" and that speed is related or proportional to the mass of the object that is warping spacetime.

that mass of an object can be represented in energy.
so you can say that the amount of energy is directly proportional to how much it warps space time.
and i would suggest that there is an energy level that is critical when hit that warps spacetime to the point that the free fall speed toward it is equal to the speed of light.
now as you add more energy, the free fall speed will no longer increase past the speed of light, however, the event horizon (the crital place where the free fall speed is equal to the speed of light). that event horizon will expand outward. I would assume that the outward expansion is limited to being proportional to rise in energy that is warping spacetime.
which would suggest that the more energy you have past the point where an event horizon is created, the further out that event horizon reaches. and this distance would be proportional to the energy that creates it.

an unfortunate side effect of this is that fact that if our astronaut fall into the gravity well and is unlucky enough to meet the event horizon, he and his ship will become energy as they fall into the event horizon. some will burst out back into space in the form of x ray and gamma ray radiation while the energy that is caught in the event horizon will be lost to the outside observer forever. some of the radiation that was traveling equaly along the event horizon will be forever doomed to a light treadmill, probably just hanging out at the edge forever, trying in vain to escape.

Events still happen, on the inside, the system is (the other side of the gravitational event horizon) just energy, accumulating.

don't forget, energy has no size, only charge so it is possible to have mind boggling huge amount of energy in one spot.

this energy seems to be doing work by distorting spacetime.

you asked about the distance to the "singularity" I would bet that it is proportional to the change in energy from the critical point where spacetime is warp so much that the free fall is equal to c and the total energy/mass of the "singularity"

time is still encompassing the whole system, as time seems to be universally
moving in one direction, I believe that time can be bent by gravity in relation to an outside observer just like light is bent by diffraction. you can bend it in any way you would like but you just cant go backwards and you cant stop time in your local observational "inertial" frame.

Disinfo Agent · #16 (**permalink**) 28-June-2008, 02:56 PM

Quote:

Originally Posted by tommac

OK then at this point in time ... No stars have collapsed beyond the point of the EH.

...You are correct, so long as you add "from the point of view of distant observers". At those stars, they have indeed collapsed.

Non-simultaneity -- it boggles the mind, doesn't it?

sabianq · #17 (**permalink**) 28-June-2008, 03:47 PM

i see it this way,

time is all encompassing, it marches forward and there is nothing we can do here to stop it or make it go backwards. Light is the carrier of information, not an event, only the information of an event. the event itself happens when it happens whether it was yesterday, now or a million years ago. since light can only travel at the speed of light and its speed is finite, the information that describes an event is limited to how fast that information can get from the event to an observer.

since light has a limited speed of propagation, and since light is carried by spacetime, and spacetime is influenced by gravity then it makes sense that the information of an event that is carried by the light would also be influenced by the geometry of spacetime making it look like an events time frame has changed.

Argos · #18 (**permalink**) 28-June-2008, 10:55 PM

Because it is saturday and I´m sitting idly at home recovering from a small surgery, I set out to research the question of what 'distance' is supposed to mean within a Schwarzschild BH, after having been alerted of flaws in my reasoning by a knowledgeable member.

I´ve stumbled on this great document, which has enlighted me much [it seems to be 'kosher', paraphrasing Publius], and I hope it does the same to you, Tommac. Scroll Down to "The Schwarzschild Solution".

Quote:

The fact that _r becomes timelike for r less than 2M means that “motion” in the r direction becomes the same as motion in any other timelike direction. We have no choice about the fact that our world lines run into the future, so any object that crosses the onion layer at r=2M, the event horizon, must have a world line that runs in the direction of decreasing r. That's the definition of “the future” within the event horizon.

Also, you might like to try a cool primer on 'manifolds'

tommac · #19 (**permalink**) 28-June-2008, 11:51 PM

Quote:

Originally Posted by Argos

It is the critical radius. The singularity is at the center of mass of the collapsed star.

The time as measured by your clock, which is not affected.

Hmmm ... wouldnt we see time stopped at the EH ? If time is stopped how can anything progress with respect to time?

Also ... I may want to argue that the center of mass can not collapse to a point but rather represented by the EH itself. I am not sure about this yet though. The train of thought here is that the BH is not really 3d ( or 4d ) .. but rather a complex 2d object that is always a circle that is perpendicular to the line of sight. ( I can explain why I think this if anyone cares ) but I am going a little off topic here.

tommac · #20 (**permalink**) 28-June-2008, 11:56 PM

I agree with everything you are saying ... BUT time appears to stop from our vantage point or relative to us. So in our history and our future assuming that we dont fall into a similar gravitational well ... we could conclude that it did not collapse further than the EH and that it is frozen there in time.

Quote:

Originally Posted by Tim Thompson

Actually, no it doesn't. The whole point of the "coordinate singularity" is that it is only an illusion. Despite the title "relativity" we must remember that events are absolute. Everything that happens in one reference frame happens in all reference frames. If one observer sees something blow up, all observers will see it blow up. If two things smash into each other in one reference frame, they will smash into each other in all reference frames. And if something falls into the black hole in one reference frame, it will fall into the black hole in all reference frames. It only "looks like" things don't fall in, it only "looks like" time stops, but it is no more correct to say that time actually stops than it is to say that an optical illusion is real because we can see it. What we "see" is not reality, what really happens is reality.

tommac · #21 (**permalink**) 29-June-2008, 12:10 AM

I ma not really sure i follow what the first half of your post has to do with my question but this part seems to so let me address this

Quote:

Originally Posted by sabianq

you asked about the distance to the "singularity" I would bet that it is proportional to the change in energy from the critical point where spacetime is warp so much that the free fall is equal to c and the total energy/mass of the "singularity"

time is still encompassing the whole system, as time seems to be universally
moving in one direction, I believe that time can be bent by gravity in relation to an outside observer just like light is bent by diffraction. you can bend it in any way you would like but you just cant go backwards and you cant stop time in your local observational "inertial" frame.

A clock at the EH of a black hole would never move if we were observing it from earth. it would move if we were wearing it at the EH ... but there are no new events for the clock while viewing it from our vantage point.

tommac · #22 (**permalink**) 29-June-2008, 12:16 AM

Quote:

Originally Posted by Disinfo Agent

...You are correct, so long as you add "from the point of view of distant observers". At those stars, they have indeed collapsed.

Non-simultaneity -- it boggles the mind, doesn't it?

Agreed! Just wanted to make sure i was looking at it correctly. Now wouldnt that mean that the EH is the singularity as viewed by us? ... let me fill in that jump of logic that i just made.

If time stopped ... then for the SOL to remain constant space must also be infinitely compressed basically to 0 thickness ... that means that a BH has 0 volume relative to us. In a previous post on this thread I mentioned that I believe a BH to be 2d basically a circle that is perpendicular to any and all lines of site it also seems to not have any time thus it is 2d ... Does this seem reasonable?

tommac · #23 (**permalink**) 29-June-2008, 12:26 AM

I get this ... however ... I am not sure if this answers my questions.
At the EH time relative to us stops. If time stops relative to us then relative to us no additional events will happen to anything that reaches the EH. It is stuck there forever. However it also takes up 0 space. So there is no worry about something crashing into the back of the spaceship.

Quote:

Originally Posted by Argos

Because it is saturday and I´m sitting idly at home recovering from a small surgery, I set out to research the question of what 'distance' is supposed to mean within a Schwarzschild BH, after having been alerted of flaws in my reasoning by a knowledgeable member.

I´ve stumbled on this great document, which has enlighted me much [it seems to be 'kosher', paraphrasing Publius], and I hope it does the same to you, Tommac. Scroll Down to "The Schwarzschild Solution".

Also, you might like to try a cool primer on 'manifolds'

sabianq · #24 (**permalink**) 29-June-2008, 01:48 AM

Quote:

Originally Posted by tommac

I ma not really sure i follow what the first half of your post has to do with my question but this part seems to so let me address this

A clock at the EH of a black hole would never move if we were observing it from earth. it would move if we were wearing it at the EH ... but there are no new events for the clock while viewing it from our vantage point.

when you are looking at an event. say the clock from such a different observational frame, say earth. You are not looking at the actual event (the clock) you are looking at a "picture" or movie of the clock. you are loomking at the information in the wave of light that represents the clock. in reality, you can never actually look at anything because the light takes "time" to reach your eyes.

light that carries that information is warped and distorted by gravity. this caused abberations (spelling)? in the information you see.

tommac · #25 (**permalink**) 29-June-2008, 02:19 AM

How about if someone brings the clock back ... spaceship leaves with a clock then brings the clock back ... or say twins one goes on a journey at near the speed of light or near a deep gravity well? Please open up another thread to discuss your interpretation of GR. We are getting off topic from my initial question.

Quote:

Originally Posted by sabianq

when you are looking at an event. say the clock from such a different observational frame, say earth. You are not looking at the actual event (the clock) you are looking at a "picture" or movie of the clock. you are loomking at the information in the wave of light that represents the clock. in reality, you can never actually look at anything because the light takes "time" to reach your eyes.

light that carries that information is warped and distorted by gravity. this caused abberations (spelling)? in the information you see.

sabianq · #26 (**permalink**) 29-June-2008, 02:54 AM

I am truly sorry,
I thought your question was

"What is the difference between an event horizon and a singularity?"

the answer i supplied was that an event horizon is nothing more than a boundary force where the gravitational force which is the nominal acceleration due to gravity of the object/mass/energy is equal to the speed of light.

and a singularity is the mass/energy that is responsible for the gravitational force.

the nominal acceleration due to gravity is directly proportional to the mass of the object (say a planets or stars mass)

the gravitational field strength should be inversely proportional to the square of the distance from the source of gravitational field.

the distance of the event horizon from the source should be equal to the distance where the gravitational acceleration is equal to c.

sabianq · #27 (**permalink**) 29-June-2008, 02:57 AM

Quote:

Originally Posted by tommac

How about if someone brings the clock back ... spaceship leaves with a clock then brings the clock back ... or say twins one goes on a journey at near the speed of light or near a deep gravity well? Please open up another thread to discuss your interpretation of GR. We are getting off topic from my initial question.

I was just suggesting an answer to your question.

what do you think?

this your thread,

sabianq · #28 (**permalink**) 29-June-2008, 03:12 AM

Quote:

Originally Posted by tommac

How about if someone brings the clock back ... spaceship leaves with a clock then brings the clock back ... or say twins one goes on a journey at near the speed of light or near a deep gravity well?

this is a pretty good site to look at
http://en.wikipedia.org/wiki/Twin_paradox
http://findarticles.com/p/articles/m...9/ai_n15400032
http://physics.suite101.com/article....e_twin_paradox
http://www.einsteins-theory-of-relat...n-paradox.html
http://www.sciam.com/article.cfm?id=...lativity-theor
http://imagine.gsfc.nasa.gov/docs/as...s/971109a.html
http://www.npl.washington.edu/AV/altvw38.html
http://physics.ucsc.edu/~drip/SRT/sec04.pdf

hope this helps

tommac · #29 (**permalink**) 29-June-2008, 06:05 AM

You should be set ... let me know.

Quote:

Originally Posted by sabianq

this is a pretty good site to look at
http://en.wikipedia.org/wiki/Twin_paradox
http://findarticles.com/p/articles/m...9/ai_n15400032
http://physics.suite101.com/article....e_twin_paradox
http://www.einsteins-theory-of-relat...n-paradox.html
http://www.sciam.com/article.cfm?id=...lativity-theor
http://imagine.gsfc.nasa.gov/docs/as...s/971109a.html
http://www.npl.washington.edu/AV/altvw38.html
http://physics.ucsc.edu/~drip/SRT/sec04.pdf

hope this helps

tommac · #30 (**permalink**) 29-June-2008, 06:16 AM

Quote:

Originally Posted by sabianq

I was just suggesting an answer to your question.

what do you think?

this your thread,

I was just commenting on your off topic ( off OP ) discussion about light being the carrier of information and the reason that time appears to be off. Unless I understood you incorrectly I dont understand how light would come into play if a two twins would age differently. Again this is pretty off topic from my initial question and I would prefer that you create your own thread to discuss/defend your ATM.

Quote:

Originally Posted by sabianq

when you are looking at an event. say the clock from such a different observational frame, say earth. You are not looking at the actual event (the clock) you are looking at a "picture" or movie of the clock. you are loomking at the information in the wave of light that represents the clock. in reality, you can never actually look at anything because the light takes "time" to reach your eyes.

light that carries that information is warped and distorted by gravity. this caused abberations (spelling)? in the information you see.

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