How do Black Holes exist with Relativity?

I'm terribly confused. In your opening post you tell us all your understanding of black holes is limited to illustrations aimed at high-school students, and yet now you're telling us the solutions to variational problems on curved manifolds. Is this your mathematics, or someone else's? (The equation you've posted is relevant for an observer in r>2M watching the motion of an infalling massless particle with no angular momentum).

It doesn't really matter, given it's clear you don't understand what's written. Had you known what you're on about, or even studied the tiniest bit of GR, you'd know that if you want to describe physics in a neighbourhood of the event horizon, then the standard Schwarzchild coordinates are no good. There's no globally defined chart, and in particular the standard coordinates are no good at r=2M. Kruskal coordinates are convenient for such a job.

Maybe now I've given you a convenient coordinate system to use, you'd like to show us the corresponding calculation.

 

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Guest254: Umm, no, I didn't "rediscover" the Schwarzschild metric or this derivative; you would prefer I did? I didn't post that to prove something to you, and my responses are not directed toward you. When I said "yours is not the mind I am probing" I was politely saying your knowledge/participation does not interest me, thanks. :shrug:

On your first point, isn't it well established that shell theorem isn't completely valid in Relativity? I wasn't suggesting otherwise; I was speculating on why we observers on Earth might see regions that have characteristics of what we call a black hole, even if no singularity "currently" resides within it. On your second point, I think you're right in a sense in that the entire region within the Schwarzschild radius would be "on the cusp" of collapse but when you say that tiny black holes would form you are speaking from a frame local to the collapsar, which again would have a distant coordinate time of infinity...

 

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I felt it unlikely that you'd actually done the mathematics. I think I said to you a while back that I'd translate some physics from some mathematics for you, if you'd meet me half way and learn some basic general relativity. Unsurprisingly, it seems you've bailed on your side of the bargain.

For the love of God - why don't you people spend your time a little more productively by actually learning about the areas of physics you like to harp on about!!

 

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Then I've got some good news for you. I've been reading books (some pop-sci and some a bit more advanced), and tomorrow is my first day back at UNL for Physics. Unfortunately, dealing with old, unhappy graduates who try to derive their self-worth by pointing out how stupid others are is not something that I intend to do after I finish my degree.

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So does this mean you can do some basic relativity? After all, you've told us that you'd already done the maths - from which we can only infer you're able to do the relevant GR calculations.

I've given you a convenient coordinate system to use (google Kruskal coordinates), so when you feel like flexing your GR muscles, let us know and post the calculations here.

 

Slow down, chief. You said

What calculation were you referring to, specifically? And in what post did "people" tell me how to do it? And who claims that the calculation is wrong...you? I showed the equation from which I deduced that the distant observer calculates the black hole to form at t=infinity. Why you think this means that I'm claiming to know more than I do I have no idea. I know there are other coordinate systems (Kruskal, Lemaitre, et al); are you saying that if the calculation is made in Kruskal coordinates that the infinitely distant observer will calculate a finite time for the black hole formation?

 

RJBerry, you're the one who said you've done the math. Now you seem to be back tracking and saying "Where did anyone tell me how to do it?". Well if you understand the formulae you posted you'd know how to do it. And well done on being able to Google for other well known coordinates in GR, now let's see if you can do something with them.

 

In response:

You have claimed an event does not happen, i.e. a particle cannot cross the event horizon. This is false. It is a simple exercise to go to the frame of an infalling test particle and show the time experienced by that particle until it crosses the event horizon is finite. You say you've done the math - then you should know this.

I have given you a coordinate system valid in a neighboorhood of the event horizon - this means there are no coordinate singularities in the region in which you want to do physics.

You've done no calculation.

Makes no sense.

Show us your calculation. You have the Schwarzchild metric and a variational principle, so if you've done the calculation you've derived the relevant geodesic equations and done some integrals. Show us.

Firstly, I don't believe for a second you're at all familiar with those things. But prove me wrong - answer your own question. I don't think you'll be able to...

Why do you people do this?

 

This should encourage your curiosity a little more about Black Holes.........

http://news.yahoo.com/s/space/20090608/sc_space/arealwhopperblackholeismostmassiveknown

 

Guest254: I said the event does not happen from a particular frame, not that it does not happen at all, and I've been very clear about this. From what I can tell, Kruskal coordinates are not defined at r=infinity so the infinite observer issue is not resolved, and your ignorance is shining through your arrogant visage by telling me otherwise. I have no interest in bantering with you or the "competant" AlphaNumeric - I've told you this more than once so please go away.:bugeye:

 

It now seems that you're unaware that time is frame dependent concept - I assumed you knew some basic special relativity, but perhaps I was too kind.

What's this? No calculation? Well if you people are anything, it's predictable.

 

And we're into full blown crank territory now. You make claims you can't back up, you can that pointed out by people who can do the things you claimed you could and so all you can do it point at the fact I didn't go back and use the Firefox spell checker on my post. As if my spelling is relevant to the fact I was talking about competency in physics. For instance, I can do all the calculations Guest is asking you to do and which you claimed you'd either done or could do. I'm competent at it. Shame the same can't be said for you.

 

black-holes do they even exist

for black-holes to even exist means that gravity over-whelms the nature of the particles involved , one dimensionally , from one direction , either above or below the galactic globular center point

however I tend to focus on the particles themselves from an hydraulic point of view

in all fluid hydraulics you can only squeeze so far until you can only squeeze down so far and then the particles push back

hence a " black-hole " is not really possible , since a black-hole suggests the collapse of matter down to non existence or singularity

 

Keep thinking.........

http://www.msnbc.msn.com/id/31173519

 

Hello Thinking. Don't forget that a particle has a tiny amount of energy and the internal forces are finite. Think about how much energy and force can be brought to bear on the particles by the internal heat and pressure exerted by a massive body that GR would define as a black hole. No particle could withstand such compression without undergoing significant change I wouldn't think.

We have no way of knowing the physics that is possibly taking place within the event horizon of a black hole but mathematically they are derived from Einstein's field equations and there are lots of reasons to believe that they do exist.

 

RJ: Your posts indicates that you lack an understanding of how a Black Hole forms. The concept is very simple.

For a given amount of mass, the radius of a black hole event horizon can be calculated. I am sure that a search could locate tables relating radius to mass for black holes which do not rotate & have no charge.

When (if) 3-4 or more stellar masses are crushed by gravity into a volume less than that indicated by the calculated event horizon radius, a black hole with an event horizon is formed. The calculations relating what can be measured/seen by a distant observer are not applicable prior to the formation of the black hole & accompanying event horizon.

The above analysis does not require doing the calculations. It only requires thinking a bit.

Aside from any analysis, we have observational evidence of existing black holes. It is crazy to deny that they can form in finite time. They have formed in finite time. To the best of our knowledge, the universe is about 13-14 billions years old & there are a lot of black holes, many formed long after the birth of the universe.

To back up the views expressed in this thread, you must provide far more cogent arguments than you have so far posted. Without better arguments/analysis than you have shown so far, you deserve to be considered an intelligent crack pot or a naive child-like personality who has read & misunderstood some dumbed down articles on the subject.

 

Moderator action:

The thread "black-holes do they even exist" was merged into this thread because that thread raised exactly the same issue as that raised in this already existing thread. Please do not open multiple threads on this same topic.

 

Dinosaur: I guess I'll reply to you although I don't believe you have read all of my posts (or maybe I wasn't clear enough). Otherwise you would give me credit for more understanding than you have. Frankly I am baffled that I must resort to using TEX (first time so go easy!) than qualitatively asking my questions in order for anyone to understand me, but here it goes...

\( r = { 2Gm \over c^2 } \), with G = gravitational constant, m = mass of body; very straight forward. The "3-4 stellar masses" you refer to are determined by the mass required to generate sufficient gravitational forces to overcome the neutron degeneracy pressure.

In the frame local to the formation, I agree with this.

I don't know what you mean by "are not applicable". The Schwarzschild line element is described by
\( ds^2 = - \left( {1-{2M \over r}} \right) dt^2 + \left( {1 - {2M \over r}} \right) ^{-1} dr^2 + r^2 d\theta^2 + sin^2\theta\phi^2 \)

where the Schwarzschild coordinates are given by (t, r, \( \theta\), \( \phi\)). Granted, this is pretty heady stuff, but we don't need it to pose my question!

A derivative of this is
\( {dt \over dr} = {dt \over d\tau} {d\tau \over dr} = {- \sqrt {r \over 2M}} \left( {{1-2M} \over {r}} \right) ^{-1} \)

which describes the calculated coordinate time of an object approaching the black hole by the infinitely distant observer. Note that the observer is "infinitely distant" to simplify the equations such that he experiences no gravitation from the black hole, but the conclusions are similar for any body not traveling towards the event horizon ("static observers" I believe they are called). I did not derive this calculation, as some here believe that I should've to "prove" myself. I am not posting these things to show how far I can piss, I was only looking for discussion on the topic and an answer to my question. However, anyone with a bit of common sense can see that when r approaches x(=2M) you get

\( - {{x} \over ({1-x})} \)

Now as the radius approaches zero (as would be required "just before" the singularity initially forms), t moves to infinity. That's it. From the frame of any static observer the black hole apparently never forms (or more precisely, forms at t=infinity). D H calls it games of semantics, and if you want to blow off the question in that manner it is your prerogative, yet the question remains. The only frame in which the singularity forms is one which contains a body that actually makes the journey, and that by definition presumes that a crossable event horizon already exists!

Guest254 and AlphaNumeric claim that Kruskal coordinates magically resolve this problem. I initially deferred to their greater mathematical knowledge, but when I looked into it it appears that Kruskal coordinates are not defined at r = infinity which, unfortunately, is where our observer resides!

Arrgh, I have dealt with this issue many times in this thread. The mass in this "black hole region" remains, and the gravitational effects would still be felt. Instead of being trapped "forever", light would be detained "longer and longer", approaching an infinite time (yet all light would eventually escape).

Somehow I feel like my simple question ("Why do we believe singularities exist today from our frame?") has been inflated to being some fully fleshed out theory that I'm defending. This is not the case; I'm just asking questions and applying common sense and logic to what knowledge I can gain. If someone were to give me a satisfactory answer (or, if not, then at least acknowledge that the question is a valid one!) then I would be most grateful.

Et tu, Brute? Don't go there.

 

James R: Yes, it does help quite a bit, thank-you. My original question (question 3 in post #3) was "how can we postulate that black holes exist today?" and in that question I was defining a black hole as a region containing a singularity, although defining a black hole as a region with an event horizon is the same thing to me (i.e. one implies the other).

And you're right, I didn't mean to imply that everybody believed something, one way or the other. Later I said

Note: "many folks" apparently = just about every poster in this thread (including one who "felt compelled to storm on in" and call me "stupid"), except you and myself, so I don't think the assumption was completely unwarranted.:shrug: