/sci/ - Science & Math

>>11600410
Therefore, invoking a "big bang" to attempt to circumvent the violation of the usual conservation laws is a circular argument and therefore completely invalid.

Furthermore, Einstein's field equations are nonlinear and so the principle of Superposition doesn't hold in General Relativity. But it does hold in Newton's theory.

Thus if X and Y are two different solutions to Einstein's field equations, then the linear combination of aX + bY, where a and b are scalars, isn't a solution. Physically this means that one can't simply pile up masses and radiation in any given spacetime to obtain multiple masses and radiation. Additionally, there are no solutions to Einstein's field equations for two or more masses and there is no existence theorem by which it can even be asserted that the field equations contain latent solutions for two or more masses. Thus it's not possible to insert a black hole universe into a big bang universe or into another black hole universe, or to insert a big bang universe into a black hole universe or another big bang universe.

Nevertheless, Einstein's followers routinely and incorrectly claim the existence of multiple black holes from objects such as stars by means of irresistible gravitational collapse.

Now read pic related if you want to understand all of this in depth.

faggot

i'll do this shit all day with you

>>11600414
Mr. C. adds more claims to this: In our modern notation, a radial coordinate r is used to describe the Schwarzschild solution, the prototype of a black hole. "That’s not a radial distance!", he shouts. "To get the radial distance you have to integrate the square root of the radial component grr of the metric!!" Now that happens to be right, but a non-issue; in practice we use r just because it is a more convenient coordinate, and every astrophysicist knows that an accurate calculation of the radial distance, if needed, would be obtained by doing exactly that integral. "r is defined by the inverse of the Gaussian curvature", C continues, but this happens to be true only for the spherically symmetric case. For the Kerr and Kerr-Newman metric, this is no longer true. Moreover, the Gaussian curvature is not locally measurable so a bad definition indeed for a radial coordinate. And why should one need such a definition? We have invariance under coordinate transformations. If so desired, we can use any coordinate we like. The Kruskal-Szekeres coordinates are an example. The Finkelstein coordinates another. Look at the many different ways one can map the surface of the Earth on a flat surface. Is one mapping more fundamental than another?
"The horizon is a real singularity because at that spot the metric signature switches from (+,-,-,-) to (-,+,-,-)", C continues. This is wrong. The switch takes place when the usual Schwarzschild coordinates are used, but does not imply any singularity. The switch disappears in coordinates that are regular at the horizon, such as the Kruskal-Szekeres coordinates. That’s why there is no physical singularity at the horizon.

>>11600414
But where does the black hole mass come from? Where is the source of this mass? R μν = 0 seems to imply that there is no matter at all, and yet the thing has mass! Here, both L and C suffer from the misconception that a gravitational field cannot have a mass of its own. But Einstein’s equations are non-linear, and this is why gravitational fields can be the source of additional amount of gravity, so that a gravitational field can support itself. In particle theories, similar things can happen if fields obey non-linear equations, we call these solutions "solitons". A black hole looks like a soliton, but actually it is a bit more complicated than that.

The truth is that gravitational energy plus material energy together obey the energy conservation law. We can understand this just as we have explained it for gravitational waves. And now there is a thing that L and C fail to grasp: a black hole can be seen to be formed when matter implodes. Start with a regular, spherically symmetric (or approximately spherically symmetric) configuration of matter, such as a heavy star or a star cluster. Assume that it obeys an equation of state. If, according to this equation of state, the pressure stays sufficiently low, one can calculate that this ball of matter will contract under its own weight. The calculation is not hard and has been carried out many times; indeed, it is a useful exercise for students. According to Einstein’s equations, the contraction continues until the pressure is sufficiently high to stop any further contraction. If that pressure is not high enough, the contraction continues and the result is well-known: a black hole forms. Matter travels onwards to the singularity at r = 0, and becomes invisible to the outside observer.

>>11600414
All this is elementary exercise, and not in doubt by any serious researcher. However, one does see that the Schwarzschild solution (or its Kerr or Kerr-Newman generalization) emerges only partly: it is the solution in the forward time direction, but the part corresponding to a horizon in the past is actually modified by the contracting ball of matter. All this is well-known. An observer cannot look that far towards the past, so he will interpret the resulting metric as an accurate realization of the Schwarzschild metric. And its mass? The mass is dictated by energy conservation. What used to be the mass of a contracting star is turned into mass of a "ball of pure gravity". I actually don’t care much about the particular language one should use here; for all practical purposes the best description is that a black hole has formed.

But has it really? Isn’t it so that the collapsing star hangs out forever at the horizon? Well, in terms of the Schwarzschild coordinates, this is formally true! The Schwarzschild solution is the asymptotic limit of the solution in the forward time direction. At finite times, the region behind the horizon does not exist. However, for this analysis, one can better use the Eddington-Finkelstein coordinates, where one does notice that the future part of the horizon does exist. This discussion is compounded a bit because the construction of the maximal extension of spacetime is subtle, and it is certainly not understood by C. Think of a map of the North Pole of the Earth, where it could be that coordinates were chosen such that they cannot be extended across the equator. Formally, the equator is then a horizon. But nobody who’s walking on the equator has any trouble with that.

what the fuck is happening

>>11600506
>>11600507
>>11600510
>quoting Hooft

Bad idea, anon.

Hooft has been demonstrated over and over again to not actually understand what he's talking about, and all of his claims (including the ones made in the very section you refer to on Hooft's site) have been properly debunked already. For a thorough scientific response to Hooft's claims, see: https://files.catbox.moe/9u2rm3.pdf and also here: https://files.catbox.moe/uzvzkh.pdf

>>11600506
>>11600507
>>11600510
>quoting Hooft

Bad idea, anon.

Hooft has been demonstrated over and over again to not actually understand what he's talking about, and all of his claims (including the ones you quote from on Hooft's site) have been properly debunked already. For a thorough scientific response to Hooft's claims, see: https://files.catbox.moe/9u2rm3.pdf and also here: https://files.catbox.moe/uzvzkh.pdf

>>11600520
Where are any of the facts I posted debunked?

>>11600524
You copypasted text from Hooft who takes things out of context and ignores scientific facts whenever it suits him. His statements have been properly dealt with in the papers I linked.

>>11600543

>>11600543
Where in the papers you linked? I don't see anything debunking the facts I posted. I doubt you even understand 10% of what you're posting.

>>11600565
First PDF is a 104 page document dealing with what Hooft said in depth - in other words, all of it deals with the "facts" you posted.

You can use ctrl+F and search parts of the text you copypasted if you want to see something specific. For example ctrl+F the following:

where does the black hole

>>11600584
>First PDF is a 104 page document dealing with what Hooft said in depth - in other words, all of it deals with the "facts" you posted.
You keep saying this without presenting any actual proof. You're not lying are you?

>>11600590
See: >>11600584

>>11600591
See >>11600590

>>11600590

are you dense? he gave you a huge document full of scientific facts.

For your own sake hopefully one day you'll be able to overcome your refusal to look at the facts.

>>11600606
It's certainly a huge document, but it's filled with rambling nonsense that doesn't even address the points I posted. Just give me one example of a debunk of anything T'Hooft said and I'll admit black holes don't exist.

People who don't know how to Ctrl+F really shouldn't be posting on this mongolian stamp collector forum.

>>11600641
People who don't understand their own sources, to the point where they can't even come up with a single example showing what they claim, should not post them. Crothers is a crank gardener who has no clue what he's talking about. If you can't understand his paper you certainly can't understand actual physics.

>>11600410
How do you explain:

CMB
hubble flow
the great agreement between [math]\Alpha[/math]CDM model and CMB power spectrum
gravitational redshift in agreement with predictions of GR
gravitational waves in agreement with predictions of GR
large-scale structure of universe in agreement with predictions of GR
distribution of atom species in agreement with big-bang nucleosynthesis
gravitational lensing in agreement with GR predictions
deflection of light around massive bodies in agreement with GR predictions
astronomical observations of black holes

without Einstein gravity and hot big bang cosmology?

>>11600414
You're not seriously expecting the average /sci/entist to comprehend this are you?

>>11600691
It's incredibly easy to comprehend.

For example, the second section is based on a freshmen level mistake in confusing the escape velocity beyond the event horizon (greater than the speed of light, meaning there is no possibility of escape) with the escape velocity at the event horizon (the speed of light). The stupidity of this error indicates the author has no clue what he's talking about.

>>11600520
This.

>>11600410
>All alleged "black hole" models pertain to a universe that is spatially infinite, is eternal, contains only one mass, is not expanding, and is asymptotically flat or asymptotically not flat.
Wrong. Stopped reading there.

>>11600776
That's what their equations are saying.

>>11600778
Wrong.

Great minds focus on ideas and science, small minds >>11600650 obsess over people and personalities.

>>11600781
Correct. See:

https://www.youtube.com/watch?v=6zWy6_Mog70

https://www.youtube.com/watch?v=ev10ywLFq6E

https://www.youtube.com/watch?v=QBorBKDnE3U

Also read: https://files.catbox.moe/b3aur6.pdf

>>11600814
>Great minds focus on ideas and science
Then OP is not a great mind, since he refuses to discuss anything he posts, indicating he doesn't understand it.

>>11600410
>SCIENCE AND MATH