The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. In a paper, George Ellis et al. (2010) review an old proposal of replacing Einstein's Field Equations by their trace-free part (the Trace-Free Einstein Equations), together with an independent assumption of energy--momentum conservation by matter fields. While this does not solve the fundamental issue of why the cosmological constant has the value that is observed cosmologically, it is indeed a viable theory that resolves the problem of the discrepancy between the vacuum energy density and the observed value of the cosmological constant. Therefore they confirm that no problems arise in such a scheme: hence, the Trace-Free Einstein Equations are indeed viable for cosmological and astrophysical applications.
So what do you think? Can the Trace-Free Einstein Equations be a Viable Alternative to General Relativity? Your comments are welcome
Do you happen to know if the standard model stress-energy tensor is traceless? As I recall the EM part is. If the full SM were traceless then I would think this mod to GR would make great sense.
The Standard Model stress-energy tensor isn't traceless, since not all particles are massless. The strress-energy tensor for the electromagnetic field alone is traceless, since the photon is massless. But, of course, this isn't enough. The electromagnetic field is a free field, but interactions with matter fields will lead to a non-zero beta-function (cf. QED). Similarly for the other sectors of the Standard Model.
In any case, this doesn't affect the issue of the cosmological constant, since this is an allowed term in the Einstein-Hilbert action and there isn't any symmetry that makes it vanish and classical considerations are only sensitive to the ratio of the cosmological constant to the-appropriately scaled-Newton constant.
Indeed, there isn't any reason that would imply that the vacuum expectation value of the matter stress-energy tensor should be equal to the contribution of the cosmological constant term to the Einstein equations: the two are independent contributions. Once one does have a matter contribution, it's not possible to invariantly say what fraction of the part proportional to the metric is due to matter and what part is due to the cosmological constant.
This paper by G. Ellis is published in Class.Quant.Grav. 28 (2011) 225007, you can find it on arXiv:1008.1196 and it contains lots of references to work done on this idea. The usual term for it is unimodular gravity.
Ellis et al are still barking up the wrong tree. None of the following are altered by using the traceless.
(1) The cosmologists claim that a finite mass produces infinite gravity. Here are just a few examples. According to Hawking [1],
“The work that Roger Penrose and I did between 1965 and 1970 showed that, according to general relativity, there must be a singularity of infinite density, within the black hole.”
According to Carroll and Ostlie [2],
“A nonrotating black hole has a particularly simple structure. At the center is the singularity, a point of zero volume and infinite density where all of the black hole’s mass is located. Spacetime is infinitely curved at the singularity. . . . The black hole’s singularity is a real physical entity. It is not a mathematical artifact . . .”
According to Dodson and Poston [3],
“Once a body of matter, of any mass m, lies inside its Schwarzschild radius 2m it undergoes gravitational collapse . . . and the singularity becomes physical, not a limiting fiction.”
According to Penrose [4],
“As r decreases, the space-time curvature mounts (in proportion to r−3), becoming theoretically infinite at r = 0."
I could cite many more sources but the above is sufficient.
Thus, as I previously remarked, it is claimed by the cosmologists that a black hole has a finite mass, that this mass concentrated at its ‘singularity’ at the ‘centre’ where r = 0, where density is infinite and spacetime curvature infinite. Since Einstein’s gravity is not a force but instead spacetime curvature, the cosmologists do indeed assert that a finite mass produces infinite gravity. Since that is just bullshit, their black hole is therefore a fallacy.
Furthermore, the r = 0 they talk about is not the centre of anything, and the quantity r they talk about is neither a radius nor a distance in the relevant metric. As I said before, the ‘Schwarzschild radius’ is not the radius of anything because it is not even a distance in the relevant metric. The black hole is again a fallacy.
(2) The cosmologists assert that all black holes have and do not have an escape velocity simultaneously at the same place. Since this is impossible their black hole is again a fallacy. Here are some examples. According to the Collins Encyclopædia of the Universe [5],
“black hole A massive object so dense that no light or any other radiation can escape from it; its escape velocity exceeds the speed of light.”
According to Gerardus ‘t Hooft, Nobel Laureate [6],
“A black hole is characterized by the presence of a region in space-time from which no trajectories can be found that escape to infinity while keeping a velocity smaller than that of light.”
According to Bland-Hawthorn [7],
“A black hole is, ah, a massive object, and it’s something which is so massive that light can’t even escape. … some objects are so massive that the escape speed is basically the speed of light and therefore not even light escapes. … so black holes themselves are, are basically inert, massive and nothing escapes.”
According to Hawking [1],
“I had already discussed with Roger Penrose the idea of defining a black hole as a set of events from which it is not possible to escape to a large distance. It means that the boundary of the black hole, the event horizon, is formed by rays of light that just fail to get away from the black hole. Instead, they stay forever hovering on the edge of the black hole.”
According to O’Neill [8],
“No particle, whether material or lightlike, can escape from the black hole.”
According to Chandrasekhar [9],
“The problem we now consider is that of the gravitational collapse of a body to a volume so small that a trapped surface forms around it; as we have stated, from such a surface no light can emerge.”
I could cite many more sources but the above is sufficient.
Thus, as I previously remarked, it is claimed by the cosmologists that a black hole has and does not have an escape velocity simultaneously at the same place. Since this too is impossible their black hole is a fallacy.
(3) The cosmologists assert that there are black holes all over the place, inside some unspecified big bang universe. However, no alleged black hole metric space pertains to configurations of two or more masses. There are in fact no known solutions to Einstein’s field equations for two or more masses and there is no existence theorem by which two or more masses can even be contemplated by means of General Relativity. The Principle of Superposition does not hold in General Relativity, because it is a nonlinear theory. So superposition is not allowed. Let X be some supposed black hole universe and let Y be some supposed big bang universe. Then X + Y is not a universe. So from where do the cosmologists get their multiple black holes inside some big bang universe? They superpose. But that’s a really big no-no! Thus, once again, the black hole universes are fallacious, along with the big bang universes.
(4) The proponents of black holes allege an extension of Hilbert’s metric to 0
Stephen tries to prove that black holes are nonsense by appealing to a mathematically illegal operation. He quotes people having said referred to a point of zero volume and infinite density where all of the black hole’s mass is located.
Stephen (ignore my previous message) tries to prove that black holes are nonsense by appealing to a mathematically illegal operation. He quotes people having referred to a point of zero volume and infinite density where all of the black hole’s mass is located.
What is density, Stephen? It is mass per volume. So if the volume is zero any mass divided by zero will result in infinite density. The mathematical operation of dividing by zero is forbidden
Matts Roos - yes, division by zero is a big no-no! That is one of my arguments against the black hole. Division by zero is undefined, it does not produce infinity, and infinity is not even a number. Thus, you have actually affirmed my argument. The black holers divide by zero, not once, but three times to get their black holes. So they are talking bullshit. The proponents of black holes also claim infinite density by a division by zero (density = mass/volume). Now that's a fourth division by zero! See my previous post for examples, since I cite and quote a number of prominent cosmologists.
The cosmologists also claim that a finite mass produces infinite gravity. That too is cosmologist bullshit. No finite mass can produce infinite gravity.
The cosmologists adorn their black holes with the schizophrenic property of having and not having an escape velocity simultaneously at the same place. That's more cosmologist bullshit. No proponent of black holes even understands 'escape velocity'. Nothing can have and not have an escape velocity simultaneously at the same place.
The cosmologists superpose their nonsensical black hole universes with one another and with their alleged big bang creation universes. Superposition does not hold in General Relativity. By superposing they talk more bullshit. See the simple example in my previous post.
The metric upon which the cosmologists rely (Droste's metric) can't be 'extended' to generate a black hole as the cosmologists claim, to produce Hilbert's 'solution'. Hilbert's 'solution' is demonstrable claptrap. Even more layered cosmologist bullshit. See the references in my previous post.
You're finished here Matts. Everything I said in my previous post is correct. Anybody can go and check since I provided full citations for my comments. Thus, the cosmologists are indeed full of bullshit. Ellis is one of them. Here is another instance; see his book with Hawking, 'The Large Scale Structure of Spacetime'. They, quite typically, also assert in their book that Laplace's dark body is a black hole. That is bullshit too, since other than having a finite mass, the Michell-Laplace dark body does not possess any of the other properties of a black hole, and so it is not a black hole! See the references in my previous post.
If you have any problems with my citations, prove that my citations and quotes therefrom are not correct. Without more cosmologist magic, you have no chance of that.
And contrary to your claim I haven't tried to prove black holes nonsense because I have proven them nonsense, without even having to down write a single equation or raise or lower a single suffix.
Here is another revelation of the cosmologists' crap:
Wormholes: Science Fiction or Pure Fantasy?
https://www.youtube.com/watch?v=16_GuYobDZ4
No I have any problems with Stephen Crothers citations, only with his rude language. He used 7 times the word bullshit, once schizophrenic, 3 times nonsense, once claptrap and once crap.
Matts Roos - But is is crap etc. That's why I said it. Somebody has to stand up and say it because it has gone on far too long. I have no compunction about saying it, time and again.
I note you have acknowledged the veracity of my citations, but you have ignored the scientific arguments I have presented. Perhaps it is logic you also object to, along with my common parlance.
It is in fact impossible for anything to have and not have an escape velocity simultaneously at the same place. This fact alone destroys the 'black hole'.
It is in fact impossible for any finite mass to produce infinite gravity. This fact alone destroys the 'black hole'.
Turn on your TV or go to the movies and what do you see Matts? A lot more explicit than "bullshit" and "crap", any day or night of the week, before audiences of all ages. Yet you object to "bullshit" and "crap" here. And the words "schizophrenic" and "claptrap" are not common parlance, so you can scratch them off your list. I stand by "bullshit" and "crap" because they are succinct and accurate.
Now please explain to us all how a black hole can have and not have an escape velocity simultaneously at the same place (a schizophrenic property) and how a finite mass produces infinite gravity.
Here are more revelations of the cosmologists' claptrap:
Crothers, S. J., The Parallax Effect on Short Hair
https://www.youtube.com/watch?v=nXF098w48fo
And don't forget my previous citation. Here it is again:
Crothers, S. J., General Relativity: In Acknowledgement Of Professor Gerardus ‘t Hooft, Nobel Laureate,
http://vixra.org/pdf/1409.0072v2.pdf
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