How do Black Holes exist with Relativity?

That is not the question RJ asked. You are helping RJ move the goalposts. The title of the thread is "How do Black Holes exist with Relativity". No mention of singularities. In post #3 he asked

No mention of singularities. The first mention of the word singularity doesn't occur until post #12 by prometheus. RJ didn't mention singularities until post #21.

Those are very different things. Most respectable physicists, when asked whether they really think that a singularity does indeed lie at the heart of a black hole or if the fact that general relativity admits singularities indicates there is something wrong with general relativity, will agree with the latter. Ask these same physicists whether they agree or disagree with the conjecture that black holes exist and almost all will agree that black holes do exist. Just because there is a potential problem with what happens at the very heart of a black hole does not mean that black holes don't exist.

The question "Do black holes really exist" is a frequently asked question. The answer is here, in the physics FAQ: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

and here, at the black holes FAQ:
http://cosmology.berkeley.edu/Education/BHfaq.html#q4

You can find similar answers all over the internet. This question is also addressed in several books on general relativity. This leads me to wonder whether you are trolling.

In an earlier post you asked about an almost black hole. An object sent to the surface of this almost black hole will of course be compressed to the size of a grain of sand. Suppose someone discovers a gravity shield so that a capsule can be lowered to the surface of this almost black hole. Suppose that the capsule is outfitted with a powerful light source that shines forever at a constant illumination. As the capsule descends the light from the capsule will be redshifted and dimmed. Assume the light source is powerful enough so that we can see the capsule even when it is resting on the surface. What would we see in the case of (a) the almost black hole remaining an almost black hole forever versus (b) the capsule's mass triggers a gravitational collapse?

In the first case, the light from the capsule, while redshifted and dimmed, will be constant in frequency and intensity once the capsule reaches the surface. If we observed the capsule forever and counted the photons emitted from it, we would count an infinite number of photons.

In the second case, the light from the capsule will continue to redshift and dim as time passes. It will not reach a steady state. Any sensing device that has a lower frequency limit will detect a last photon from the capsule in a finite amount of time. The capsule will "wink out". Suppose we have a sensing device that is not frequency limited. While this device will see photons coming from the capsule forever, it will only count an finite number of photons. The capsule did, after all, cross the event horizon in a finite interval of time, so only a finite number of photons were emitted by the capsule before it crossed the event horizon.

 

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No, a particular derivative of one of the metric entries is that. That is not 'a derivative of the metric'. And no, it's not heady stuff, it's pretty much the first non-trivial thing you do in a GR course. You have yet to show you actually grasp the equations you're posting.

As Guest said (and is a well known fact) there's no globally defined coordinate system in the Schwarzchild space-time. Kruskal coordinates are used to cross event horizons in a consistent manner, they are not used at large distances. Anyone whose ever drawn the Penrose diagram for the Schwarzchild metric will have used them.

 

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Now convinced that you're simply copying and pasting things you don't understand. Classic stuff.

There is no such place as "r=infinity" - hell, the statement "r=infinity" makes no sense. Physicists sometimes use the abuse of language "an observer at infinity", to mean there is an observer very far away and as such we can approximate certain integrals by taking the upper limit to infinity, assuming things converge fast enough.

We have told you about Kruskal coordinates because you are say you are interested in some physics in the neighbourhood of an event horizon. The Schwarzschild metric has a coordinate singularity in this region, so we have offered you a better set of coordinates to do calculations with - i.e. to make your life easier. However, it's become apparent that you're not doing any calculations, because you don't understand even the most basic parts of general relativity.

From your subsequent posts it has become apparent that you have some severe conceptual misunderstandings of even basic special relativity. It is without doubt, that from a local frame in r>2M (note I'm saying r>2M, not "r=infinity", since any large enough radius illustrates the point), it would appear that it takes an in falling test particle an infinite amount of time to reach the event horizon. However, if one does the *incredibly simple* calculation from the frame of the in falling test particle, the time experienced by that particle to reach the event horizon is, low and behold, finite. I would urge you to derive the necessary equations from first principles, then do the relevant integrals, but it's become apparent that you're not capable of doing so (despite having told everyone you'd "done the math").

There isn't even an issue here - it's just that your complete lack of basic knowledge makes it incredibly difficult to understand these things. If you were actually interested in these things, you'd go away and spend some time learning the basics. But you wont, because that's not what cranks do. Learning and understanding takes effort and intelligence - it's just far easier for you to from from one wiki article to the next, coming on places like this, and play pretend.

 

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D H: I define a black hole as a region with a singularity. Do you have an alternative definition? To me it is a contradiction to say that singularities do not exist in a frame yet black holes do.
In other words, I find the following questions equivalent regardless of my first mention of a singularity:

vs

Also, if it's the case that this is a well known contradiction between BH and GR then why in the hell did it take over 80 posts for anyone to even admit that the question was a valid one? I've been called a stupid cranky crackpot with no knowledge and no motivation to learn, yet in the end it appears that I've been asking about a well known issue? What the hell is wrong with some people on this forum? And no, I have not seen those links before, and I did NOT know this was a well-known issue with astrophysicists, but I do now and thanks for the reference.

If the infinite observer calculation cannot be used in Kruskal coordinates then why did you give me the reference? To waste my time?

TAKE A HINT

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How about the blatantly obvious definition that

Just because you don't understand something doesn't mean it is wrong.


That general relativity admits singularities is indicative that there might be a problem with general relativity. This is one of the motivating factors for string theory, loop quantum gravity, and other theories that are attempting to find a common ground between general relativity and quantum mechanics. On the other hand, sans a few crackpots, physicists do not deny the concept of gravitational collapse. There were a few holdovers until astronomers observed things that look and act exactly like the theoretical description of a black hole.

Moderator comments
You are playing semantic games. This thread is on short notice. It will head to the cesspool in 48 hours unless you can convince me otherwise.

 

D H: You want to cesspoll a thread which deals with what you said was a well-known issue between BH and GR; an issue so foundational that it has contributed to the impetus for string theory and loop quantum gravity; an issue that some participants were clearly unaware of? Do what you want but I'm not seeing this as a cesspool candidate.

 

You are not addressing fundamental issues. You are addressing semantic issues, and well-known semantic issues at that. I provided a couple of links that address this very question in post #81. Read them. I specifically addressed your question about distinguishing a "near black hole" from a black hole in post #81. The two are very different beasts. Read post #81 and read the links cited therein.

 

I thanked you for the links, they are interesting. I'm basically done here so thanks to everyone for continuing (or affirming) my understanding, and for putting up with my ego.

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There is no such thing as an "infinite observer", or "an observer at infinity". I just explained this to you. And I also explained to you why I told you Kruskal coordinates should be used in a neighbourhood of the event horizon. And still no calculations... this is all too predictable.

You've essentially got your knickers in a twist because this thread has served as a showcase for your complete ignorance of basic results from relativity. Pull up your socks and deal with it...

 

That's not the definition GR people use. You can have black holes without singularities.

IF you'd ever actually done any GR you'd know about coordinate patches. The Schwarzchild spherical coordinates are not valid at the horizon so you use Kruskal to cross the horizon in a controlled manner and then the spherical coordinates become valid again. You swap from spherical to Kruskal and back, using each one in the realm where you know they work. That's the basic concept of coordinates in manifolds.

Done lying?

 

Yes, D H helped me realize this too, thanks. I had assumed that the singularity's existence was a presumption in the black hole's existence, which is why I interchanged {black hole, event horizon, singularity} in my questions. I wasn't trying to 'move the goal posts', I had considered all variations of my question to be equivalent. Discussing the singularity is really a red herring, though, because removing it from the black hole's definition does not resolve the issue. The problem remains if the question refers to "an event horizon", or, using D H's definition, "a region of space in which the gravitational field is so powerful that nothing, including light, can escape its pull."

As I said, I'm vaguely familiar with coordinate patches, and I understand the concept. Quick question for you (I'm speaking to AlphaNumeric) - and this is a sincere question to which I do not know the answer - what do the Kruskal coordinates say about the time it takes a body to cross the event horizon as calculated by a static observer? I am now talking about an observer "hovering" over the horizon as opposed to an infinitely distant observer...

 

Did Dr. Einstein mentioned or made comment about the black hole during his lifetime? I seem to miss it. Because in his later life, Dr. Einstein commented: "I do not know anymore my relativity..".

Moderator, Whatever I post (pertaining to Big Bang or cosmoligical constant) is honest-to-goodness scientific search..So i hope you open posted articles "Man-made nuclear bomb: one best evidence of Big Bang" and "Cosmologival constant or Big Bang". thank you.and regards..


jsalea12

7.5.09 ..

 

Please permit me to re-phrase. pertaining that illustration showing a black hole inside a cone-shaped hole (spacetime). To put plainly, the classic example of spacetime gravity of Dr. Einstein is like a trampoline wherein an object dropped in will cause a dip in the trampoline, the heavier the object dropped in, the deeper the dip. IS THIS EINSTEIN GENUINE ILLUSTRATION OF HIS SPACETIME GRAVITY? That dipping deeper and deeper into spacetime (as body collapses to a blackhole). Because, in retrospect, Einstein commented, “I cannot anymore recognize my relativity..” The classic trampoline illustration appears impossible in actual outer space. There is a more realistic interpretation of spacetime gravity of Dr. Einstein that goes hand-in-hand with attraction gravity of Newton.. .

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Regards.

Jsaldea12

75.09

 

The next nonsensical post will get a warning, jsaldea12.

The correct quote is "Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore." It was intended to be taken humorously. You have taken it seriously and you have misstated the quote in a manner that illustrates a key misunderstanding on your part of how science works. While a theory is often named after the originator, it does not belong to the originator: It is in the public domain.

Regarding the rubber sheet analogy: It is an analogy. The intent of the analogy is to illustrate the concept of gravitation to the mathematically disabled.

 

jsaldea: As D H said, the trampoline/rubber sheet analogy is just way to help people get the concept, it doesn't really mean anything. It's flawed and confusing to some because it uses gravity (which is what's causing the "dip") to explain gravity. IMO a better analogy is to stretch the center of the rubber sheet, then tie it in a knot on itself like a balloon, and let it go. What you are left with is an area of tension surrounding the knot that lessens as you move further away. It's much easier to imagine that in three dimensions than the former analogy...

 

Is there a difference since an event horizon is pretty much that definition.

If you're unfamiliar with how to compute such a thing then I question your claim you understand coordinate patches and how to do such things in the usual spherical coordinates of the Schwarzchild metric.

The answer is pretty straight forward, as Kruskal coordinates are so useful precisely because they say everything is finite in and around the event horizon of a black hole.

 

I suspect it would've taken a similar amount of effort to answer my question. If Kruskal coordinates calculate a finite time for a body to cross an event horizon by a finite-distance static observer then I will have learned something very interesting, because it's not what I would predict (or expect, rather).

 

AlphaNumeric: Reading your post again, maybe you consider it to be the answer I was looking for? What I'm asking for is a calculation, not an explanation. If it's as straight-forward as you said then I don't think it's too much to ask.

 

Why do scientists so incessantly keep advocating in mass media the idea that nothing can escape gravitational pull of black holes while we know that virtual particles can?

 

No they can't, no more than any other object. The ones that "escape" are outside the event horizon and moving with sufficient speed to overcome that gravitational pull, as could a space ship from that position.
The virtual particles are "our side" of the point of no return.