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Relative energy of a black hole.

by cragar
Tags: black, energy, hole, relative
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PeterDonis
#91
Mar1-12, 02:11 PM
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Quote Quote by TrickyDicky View Post
You cannot negate it because it doesn't appear in static solutions unless you believe our universe is static.
I wasn't intending to say that my statements about the SET only applied to the static case; they always apply (see George Jones' post and my response). I was only using the static case as a simple example that most textbooks say something about, so it might be a way to get more information about what the authors of this one were thinking.

Quote Quote by TrickyDicky View Post
It is something that has been troubling relativists from 1915 when Hilbert referred to it saying that GR generates improper energy theorems. And it hasn't been solved, as I said is at the root of many difficulties with quantum gravity.
The "improper energy theorems" bother some relativists because, as I've said in previous posts, they don't fit our intuitions about how "energy" ought to behave. Since standard GR with the standard SET the way it is accounts for all the evidence we currently have, the question of whether the improper energy theorems are a "real problem" or just a sign that our intuitions aren't a good match for this area of physics is, IMO, more a question of philosophy than physics. If we get further evidence that doesn't match the standard GR predictions, then of course that will change, as I've already said.

With regard to quantum gravity, AFAIK the reason this issue creates a problem there is that we don't know how do to quantum theory period with systems that have improper energy theorems. It's quite possible that that is a problem with the way we are doing quantum theory rather than with gravity; we may simply be using the wrong set of tools. Again, unless and until we get further evidence, IMO this is more a question of philosophy than physics.
George Jones
#92
Mar1-12, 02:24 PM
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Quote Quote by PeterDonis View Post
Agreed, I should have made that clear (thought it ought to be clear from my other posts in this thread).
I thought that this is your position. I just wanted to agree, and to give quotes that back this up.
Quote Quote by PeterDonis View Post
I don't have my copy handy to check: by "a physical role" for "disembodied" energy in the field, is he referring to gravitational waves carrying energy (for example, the binary pulsar emitting them, as has been discussed in this thread)?
Yes.
PeterDonis
#93
Mar1-12, 02:30 PM
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Quote Quote by Naty1 View Post
Maybe this "classical limit" issue is the one Peter described:
Yes, that's more or less right. Slightly further down the same Wiki page is this comment:

"In curved spacetime, the spacelike integral now depends on the spacelike slice, in general. There is in fact no way to define a global energy-momentum vector in a general curved spacetime."

It doesn't say exactly which "spacelike integral" is being talked about, but I assume they mean the continuity equation integral above. In certain special cases, a particular set of spacelike slices is picked out by the symmetry of the spacetime, and the continuity integral using that set of slices defines a "total energy" that behaves the way our "Newtonian" intuitions say energy ought to behave in the presence of gravity--it includes "gravitational energy", *and* energy is "exchanged" between ordinary matter-energy and gravitational energy in such a way that the total is conserved.

But that only holds for spacetimes where the symmetry picks out a particular set of spacelike slices: two examples are a single isolated gravitating body (the "Newtonian" case is a subcase of this), where the time translation symmetry picks out a particular set of slices, and a case like FRW spacetime, where the spherical symmetry defines a set of "comoving" observers that pick out a particular set of slices. (That's why the Usenet Physics FAQ page I linked to earlier includes this case in their discussion.)

Also, note carefully that the way "gravitational energy" enters into the continuity integral is *not* by any change in the SET's definition; it is purely due to the fact that, in curved spacetime, we use covariant derivatives instead of ordinary derivatives. That means extra terms come in due to the connection coefficients, and in certain special cases the extra terms have a simple interpretation in terms of "gravitational energy" being exchanged with ordinary matter-energy.
PeterDonis
#94
Mar1-12, 02:31 PM
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Quote Quote by George Jones View Post
I thought that this is your position. I just wanted to agree, and to give quotes that back this up.

Yes.
George, thanks for the support and clarification!
Naty1
#95
Mar1-12, 04:08 PM
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For what little it's worth, I understood George's comment as supportive...

I could not find it again, but Wikipedia has a statement to the effect that the gravitational field CANNOT be associated with any particular component of the Einstein formulation...not the metric, not the Riemann curvature, not Christoffel symbol, etc,etc
and goes to say one entity cannot take precedence over all the others in defining/representing the gravitational field. In addition, Ben Crowell has previously posted in another discussion how the gravitational field representations, and the energy therein, can be subject to varying interpretations....lost that somewhere in my notes, still looking.

These are the kind of tidbits that add clarity:

That means extra terms come in due to the connection coefficients, and in certain special cases the extra terms have a simple interpretation in terms of "gravitational energy" being exchanged with ordinary matter-energy.
Again, PeterDonis, thanks for your time and effort....I picked up a lot of good information from your posts....
Naty1
#96
Mar1-12, 04:51 PM
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To supplement George's comment from THE ROAD TO REALITY:

Peter explained that quote, I think, in earlier posts here. At least I 'got it'.

Penrose has a bit more detail immediately following George's excerpt [above]which I believe directly complements Peter's previous posts:

[for two massive bodies close together and at rest].....

.... there will be [negative] gravitational potential energy contribution that makes the total energy and therefore the total mass smaller than it would be if they are far apart. Ignoring much tinier energy effects, such a distortions of each body's shape due to the gravitational field of the other, we see that the total contributions from the actual energy momentum tensor T will be the same whether the two bodies are close together or far apart. Yet the total mass/energy will differ in the two cases and this difference would be attributed to the energy in the gravitational field itself [in fact a negative contribution, that is more sizeable when the bodies are close than when they are far apart.]
...Now let us consider that the bodies are in motion.....[he describes the Taylor-Hulse binary thingy]....The energy-momentum tensor in empty space is zero, so the gravitational wave energy has to be measured in some other way that is not locally attributable to an energy 'density'. Gravitational energy is a genuinely non-local entity. This does not imply there is no mathematical description of gravitational energy, however. Although I believe it is fair to say we do yet yet have a complete understanding of gravitational mass/energy, there is an important class of situations in which a very complete answer can be given. These situations are those referred to as asymptotically flat and they refer to gravitating systems that may be regarded as being isolated from the rest of the universe, essentially because of there very large distance from everything else. ....The work of Biondi...generalized by Sachs provided a clear cut mathematical accounting of the mass energy carried away from such a system in the form of gravitational waves and a conservation law for energy-momentum was accordingly achieved. This conservation law does not have a local character of that for non gravitational fields.....
Extending the above concepts, Penrose closes the chapter:

...There are general prescriptions for obtaining conservation laws for systems of interacting fields. These come from the Langrangian approach....very powerful,,,,despite the fact that it does not...directly SEEM to give us everything we need in the case of gravitation.....
[I even had some of the above highlighted from a few years ago....too bad I did not remember this source!]
PeterDonis
#97
Mar1-12, 05:56 PM
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Quote Quote by Naty1 View Post
Again, PeterDonis, thanks for your time and effort....I picked up a lot of good information from your posts....
You're welcome! Glad I was able to help.

Quote Quote by Naty1 View Post
Extending the above concepts, Penrose closes the chapter:
Just to expand on this a bit, I believe Penrose is referring here to Noether's theorem: if the Lagrangian of a system has a symmetry, Noether's theorem shows how to construct a conserved current from that symmetry. "Energy" in this interpretation is the conserved current associated with time translation symmetry. Most of the spacetimes discussed in this thread where a useful definition of "total energy" can be made have time translation symmetry; but there are important spacetimes that don't (for example, the FRW spacetimes), which is why this method of defining energy "does not...directly SEEM to give us everything we need in the case of gravitation", as Penrose says.
Q-reeus
#98
Mar2-12, 04:36 AM
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Quote Quote by PeterDonis View Post
Q-reeus: "I will assume when you write GW above it is not the wave but gravitational energy in a static field."
Then you assume wrongly; by "GW" I meant specifically "gravitational waves". I thought that was clear from context, but I suppose I should have spelled it out. Please re-read interpreting "GW" specifically as "gravitational waves".
But then it makes no sense. You say I should have known from context GW in #77 meant gravitational waves, not gravitational energy. If you take the trouble to trace back that discussion it was referencing to comparing possible pressure vs static field gravitational energy contributions - all in the context of that given in #45 & elaborated in #52. GW's were not involved (there were of course other discussions considering GW's role, but clearly distinct from this matter). So who's to blame for thinking you must logically have meant energy in a static field, not GW's? Maybe you had another entry in mind when writing that.
Q-reeus: "That position is 'my version of the EFE/SET in GR is Absolute Truth, if you find differently by any counterexample/counterargument whatsoever, you must be in error - end of story.'"
My position is that the *standard GR* version of the EFE/SET accounts for all the physics. So far you have given no counterexample to that claim...
Last bit is patently untrue, but I guess you forgot to insert 'that I acknowledge'.
I am not saying that your way of describing certain aspects of the physics is "wrong"; I'm only saying that it's limited to certain aspects of the physics.
Which just amounts to what I say above quoted. Any counterexample, e.g. in #45, cannot be true by definition, so why bother taking it seriously? The way you express that is a little less blatant: 'just apply the standard EFE/SET formula and all must be right. Counterexample X suggesting otherwise must thus be wrong'. This is your procedure to 'defeat' any counterargument, by referring back to the rote formula I complain about! No-win situation gauranteed. i will have another shot at breaking that cyclic dilemma in a later posting.
(1) The GR solutions for static or nearly static stars require pressure to contribute to the SET in the standard way--in other words, it's not enough just to put pressure into an equation of hydrostatic equilibrium, you also need to include pressure as a "source" on the RHS of the EFE. These solutions do a good job of predicting the observed masses and other properties of stars.
Is there actually observational evidence here? Would have thought pressure a negligible SET source in stars. Maybe neutron stars, but even there do we have convincing evidence it is needed to account presumably for maximum NS mass (less if pressure is SET source, than if not)? Have come across articles where it is admitted the eqn's of state within NS's are still not fully understood.
Q-reeus
#99
Mar2-12, 04:38 AM
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Quote Quote by George Jones View Post
...Disembodied, because, from Ryder,

We cannot, then, identify a place or places, where where the gravitational field exists and carries energy, since whether the field carries energy also depends on the frame of reference. Gravitational energy is not localisable.

This means that gravitation energy cannot be included in the stress-energy-tensor field, as this is a mapping from spacetime into the space of tensors.
Precisely confirming my suspicions given in #59.
Q-reeus
#100
Mar2-12, 04:41 AM
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Quote Quote by PeterDonis View Post
...In this case, the SET does *not* include any "gravitational field energy" (it's just the standard perfect fluid SET), but nevertheless it's commonly said that "gravitational field energy" needs to be taken into account in determining the externally measured mass M of the star.
(I've explained several times how the standard picture actually deals with this--the mass M is ultimately derived from the standard SET by solving the standard EFE, with no extra "source" terms for "gravitational field energy"--the latter just happens to be one way of describing the relationship between the mass M that appears in the metric and the standard SET that appears on the RHS of the EFE.)
Hope you can appreciate that from my pov the above is frustratingly empty. On the one hand, a clear statement that gravitational field energy Eg is specifically absent from the SET. But then go on to say it is one way of describing the relationship between measured M and the SET. But nowhere have I seen you attempt to pin down what is then gravitational "energy's" role in a 'way of describing'. What exactly is it that means anything given Eg is utterly absent from the SET? Curvature non-linearity? If so, how about just plainly say so and why, or if something else, say exactly what it is.
Q-reeus
#101
Mar2-12, 04:44 AM
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Quote Quote by PeterDonis View Post
Q-reeus: "And you go on to say GW's are included somehow in the balance despite possessing zero SET contribution themselves."

What "balance" are you talking about? I said GWs carry away energy in the sense that they can later do work on a detector; and I said that the externally observed mass of the system that emits GWs decreases. But neither of those things affect the "balance" expressed in the energy conservation equation I gave, that the covariant divergence of the SET is zero.
Not energy balance per se - I have consistently acknowledged there is at least nominally a system "energy" balance. Try the 'balance' of total system *gravitating* mass (inclusive of all energy flows including GW's) discussed particularly in #50 and #54. You here in #83 (which in turn references back to #73) have imo clearly set a trap for yourself. Gravitationally collapsed system mass M - the externally observed Keplerian *gravitating* mass, declines by your admission above. Further, by your admission, the decline is owing to GW "energy" emission - which you state clearly is not a part of SET and contributes nothing to M. So please, no appeal to a rote formula here. Admit the inescapable, basic logic - *total* system *observed* mass M thus declines. If your 'answer' is to ignore this request, understand I will feel free to draw obvious conclusions. And recall in past postings you have specifically claimed M cannot decline if all matter+energy is included. Deny that and I will gladly furnish quotes to the contrary. This is relevant to the monopole GW issue btw.
Naty1
#102
Mar2-12, 08:46 AM
P: 5,632
Q-reeus posts:

...But nowhere have I seen you attempt to pin down what is then gravitational "energy's" role in a 'way of describing'.

If you READ from posts 88 on....Tricky, my posted quotes, George Jones comments and quotes and Peter's comments explain it to the extent it can be....'non localizable', covarient derivative effects, non localizable,etc,etc ......

these are all complementary, not in conflict.

including these:

There is in fact no way to define a global energy-momentum vector in a general curved spacetime."
from Ryder
We cannot, then, identify a place or places, where where the gravitational field exists and carries energy, since whether the field carries energy also depends on the frame of reference. Gravitational energy is not localisable.
and from Penrose:
.... Although I believe it is fair to say we do yet yet have a complete understanding of gravitational mass/energy, there is an important class of situations in which a very complete answer can be given. These situations are those referred to as asymptotically flat......
I could quibble with Peter's comment about problems with energy theorems (in #91) being more 'philosophy' than physics.....but that's waaaaaaaaay too nit picky....

Q-Reeus...While I see why pervect opted out early, I am on the other hand happy to see your persistence:

" It is better to debate a question without settling it than to settle a question without debating it."
.......Joseph Joubert, the 18th century philosopher


I, for one, am 'outta' here....finally!!
John232
#103
Mar2-12, 09:05 AM
P: 249
I couldn't help but wonder if, say for instance a very large star ended up being slung around the suppermassive black hole in the center of the galaxy. Then this star ended up traveling at a very high speed straight for Earth. So then say that the relative speed of the star and its mass creates an event horizon around itself because of the relative mass that was seen from Earth. You could say that it was just the relative mass that made it look like a black hole and that any planets traveling along with the star didn't observe this relative mass so then they could orbit around the star and stay just fine. So then they send a team into the black hole to try and slow it down to prevent the destruction of Earth. They then would travel straight into the black hole at speeds close to the speed of light to prevent becoming spagitified. They then transfer into the frame of reference of the star itself so they no longer observe it being a black hole. And then they land on one of the planets and find life and decide to live there since they failed blowing up the star and live on inside this "black hole" as if they are just fine. So, then do you think something like this scenario would be possible or totally science fiction?
Q-reeus
#104
Mar2-12, 09:49 AM
P: 1,115
Quote Quote by Naty1 View Post
Q-reeus posts:




If you READ from posts 88 on....Tricky, my posted quotes, George Jones comments and quotes and Peter's comments explain it to the extent it can be....'non localizable', covarient derivative effects, non localizable,etc,etc ......

these are all complementary, not in conflict.

including these:



from Ryder


and from Penrose:


I could quibble with Peter's comment about problems with energy theorems (in #91) being more 'philosophy' than physics.....but that's waaaaaaaaay too nit picky....

Q-Reeus...While I see why pervect opted out early, I am on the other hand happy to see your persistence:

" It is better to debate a question without settling it than to settle a question without debating it."
.......Joseph Joubert, the 18th century philosopher


I, for one, am 'outta' here....finally!!
Naty1, I was fearing getting only stick from you at first, but sort of ended on a relative high - but I understand your departure. It has got a bit torrid. On your first point, I want to be clear there was no specific attacking the notion of 'non-localizability' in my query. Just can't see the connection on the specifics I raised, and non-localizability seems off the mark in that respect. Just want a clear statement as to whatever connections are implied. May have missed something earlier but can't recall it. Anyway you have inspired me to soldier on, so good!
PeterDonis
#105
Mar2-12, 10:11 AM
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Quote Quote by Q-reeus View Post
Last bit is patently untrue, but I guess you forgot to insert 'that I acknowledge'.
The insertion would not change the truth value, I suppose. But you apparently don't understand what is actually required for a counterexample. A counterexample would look like this: "Here's an actual physical observable that the standard EFE/SET method doesn't predict or explain." Or: "Here's a prediction made by the standard EFE/SET method that doesn't match this actual physical observable." You have given no such example, because you have never actually tried to figure out what the standard EFE/SET method predicts or explains; you haven't used it. You've insisted on reasoning from your own set of premises (like "gravity gravitates") instead, and then you've tried to claim that if the conclusions you reach don't appear to be consistent with the standard EFE/SET method, the standard method must be wrong. So it's not that I'm saying any counterexample must be wrong by definition: I'm saying you have not actually given counterexamples at all; instead you've given conclusions derived from a different set of premises altogether, and those premises are only approximately true (and even that is only in a limited domain).

Quote Quote by Q-reeus View Post
Maybe neutron stars, but even there do we have convincing evidence it is needed to account presumably for maximum NS mass (less if pressure is SET source, than if not)? Have come across articles where it is admitted the eqn's of state within NS's are still not fully understood.
Neutron stars are a good example of pressure contributing significantly to the SET, yes. And yes, the maximum NS mass is one area where the pressure contribution is important; we know that even though we don't know the exact equation of state (because we've tested a whole range of possible equations of state numerically).

Quote Quote by Q-reeus View Post
Hope you can appreciate that from my pov the above is frustratingly empty. On the one hand, a clear statement that gravitational field energy Eg is specifically absent from the SET. But then go on to say it is one way of describing the relationship between measured M and the SET. But nowhere have I seen you attempt to pin down what is then gravitational "energy's" role in a 'way of describing'. What exactly is it that means anything given Eg is utterly absent from the SET? Curvature non-linearity? If so, how about just plainly say so and why, or if something else, say exactly what it is.
I appreciate that things look this way from your pov. But now consider how they look from my pov. As I've said several times now, in the standard EFE/SET picture, there is no *need* for the concept of "gravitational energy" at all. All physical predictions can be made without ever using it. So from my pov, the problem is not that I'm not answering your questions, but that you insist on asking them even though I've repeatedly said that they are based on the wrong set of concepts. I have been trying to meet you halfway by at least trying to express how one *might* salvage some kind of correspondence between the concept of "gravitational energy" and the standard EFE/SET method, in a limited domain. But that's only because I understand that the concept of "gravitational energy" has intuitive force, so I'm willing to expend some effort in trying to explore it and its limits.

But asking for what "exactly" the concept of "gravitational energy" means is asking too much: the concept is only a heuristic one and it does not have an "exact" meaning. (Or perhaps a better way to say this would be: one could give an exact definition of "gravitational energy", such as the Landau-Lifgarbagez pseudotensor, but no such definition is unique, and any such definition only "makes sense", only corresponds to our intuition, in a restricted set of cases.) If you want an exact answer, it is this: there is no "gravitational energy" in the SET, so as far as exact calculations of physical predictions are concerned, it doesn't exist. (You'll note, in this connection, that nobody uses any definition of "gravitational energy" to actually make physical predictions: they all use the standard EFE/SET method, and then once they know what the answer is, they overlay their chosen concept of "gravitational energy" on top of it to help them understand intuitively what's going on.)

Quote Quote by Q-reeus View Post
Admit the inescapable, basic logic - *total* system *observed* mass M thus declines. If your 'answer' is to ignore this request, understand I will feel free to draw obvious conclusions. And recall in past postings you have specifically claimed M cannot decline if all matter+energy is included. Deny that and I will gladly furnish quotes to the contrary. This is relevant to the monopole GW issue btw.
All right, let's look at this from an *exact* point of view. The exact point of view is this: the "total system" is the entire spacetime, including the region "at infinity". This "total system" does not *have* a "mass M". The exact metric is not in any of the forms where "M" even appears; it's more complicated. (One could try to extract a "piece" of the metric where a coefficient "M" appears, but that's just an approximation-see below.) So from the "exact" point of view, there is *nothing* in the physics corresponding to "total system observed mass". There is a metric at each event, and there is an SET at each event (nonzero in the interiors of the two pulsars themselves, zero everywhere else--if we ignore the EM radiation emitted by the pulsars and assume the only "radiation" in the spacetime is GWs), and the EFE holds at each event. That's it.

Does this "total system" have a "total energy"? It depends on how you define "energy". The spacetime as a whole does not have a time translation symmetry, so we can't define "energy" that way. The spacetime *may* have a continuous set of spacelike slices that match up well enough with what symmetry does exist (for example, maybe the slices are good approximations to "natural" ones that observers hovering at a large radius R above the binary pulsar system would pick out as "surfaces of constant time") to be useful in defining "energy" by integrating the energy conservation equation (i.e., the covariant divergence of the SET) over each spacelike slice. This could define a "total energy" for the system, and this total energy could turn out to be conserved (i.e., the same on every slice), at least to a good enough approximation (the same level of approximation to which the slices are good "surfaces of constant time" for some set of observers). But will this "conservation of energy" be "exact"? Probably not, since the spacetime does not have any exact symmetry. So if you want an exact answer, it is that there is no "total energy".

Now, suppose I decide to draw a boundary at some finite radius R around the binary pulsar system, and say that inside that boundary is "the total system" and outside it is "the rest of the universe". I can pick R large enough that, to a good approximation, the binary pulsar system "looks like" a simple gravitating body with some mass M. More precisely: the metric at R is still not quite in the Schwarzschild form, because the spacetime is not spherically symmetric or static; but it will be close enough that I can "split" it, approximately, into two pieces: a "Schwarzschild" piece and a "gravitational radiation" piece. The Schwarzschild piece, to a good approximation, will look like a gravitating body with a mass M that slowly decreases with time ("time" meaning "proper time according to an observer hovering at radius R). The gravitational radiation piece will be oscillating in quadrupole fashion, and could be measured by, for example, letting the oscillations heat up a detector and measuring the energy taken up. We could then, in principle, do an energy balance: the decrease in M is balanced by the energy carried away by GWs.

Will this energy balance be "exact"? Probably not, because the split of the metric into the two pieces probably won't be exact; there will probably be extra terms in the metric that are left out--they aren't included in either the Schwarzschild or the GW piece--because they are small compared to both of those pieces.

So we come back again to what I said above: if you insist on an "exact" answer, then it is this: "gravitational energy" doesn't exist, and the only exact "energy conservation" is what I said earlier: the covariant divergence of the SET (the standard SET) is zero at every event. Anything else is approximate, and breaks down if you try to press it too hard. That includes things I've said previously (like "M cannot decline if all matter-energy is included"); I apologize if I didn't make it clear enough that I was only speaking approximately.
TrickyDicky
#106
Mar2-12, 10:42 AM
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Quote Quote by PeterDonis View Post
A counterexample would look like this: "Here's an actual physical observable that the standard EFE/SET method doesn't predict or explain .
Does dark matter qualify?
PeterDonis
#107
Mar2-12, 10:58 AM
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Quote Quote by TrickyDicky View Post
Does dark matter qualify?
No. "Dark matter", from the standpoint of the EFE/SET, is just ordinary "matter" (i.e., it has the same kind of SET as the matter we observe every day) that doesn't interact with anything else non-gravitationally, so we have no way of observing it the way we observe ordinary matter, by EM radiation or any other type of non-gravitational radiation or interaction; the only way we know it's there is indirectly, through its gravitational effects.

I realize that there is an ongoing debate in astronomy as to whether the standard interpretation of observations (like galaxy rotation curves) as signifying the presence of "dark matter" is correct. There are alternate theories that modify the way gravity works (i.e., they are *not* standard GR) in order to account for the observations without postulating dark matter. I am not saying those alternate theories have been proven wrong; they haven't (I consider them all much more unlikely than the standard interpretation, but that's just my opinion). I'm just saying that the observations, by themselves, are not counterexamples to standard GR: standard GR can account for them perfectly well, by just adding the dark matter to the total SET that is being used in the EFE.

I realize also that the above is open to another objection: well, sure, you can make any set of observations compatible with standard GR by [Edit: fixed typo, was "but"] just fiddling with the SET. First of all, that's not quite true; mathematically, it can be done, yes--you can postulate any tensor you like as an "SET", put it on the RHS of the EFE, and solve for the metric it will produce--but the results may not be very reasonable physically (for example, they may violate energy conditions or other constraints that are widely accepted). Dark matter doesn't do that: the dark matter SET, as I said, is just like that of ordinary matter, so it's perfectly reasonable physically.

Second, dark matter fits into the picture in multiple places, not just one; for example, the current "best fit" big bang model requires cold dark matter, in roughly the same proportions ("roughly" because all of these calculations have significant "error bars" at our current level of knowledge) as are required to explain the galaxy rotation curves and other "local" observations. So dark matter is not just being put in ad hoc to fit one piece of data; it has a reasonable place in a comprehensive model, and that comprehensive model uses the standard EFE/SET of GR. (That's one reason, btw, why I think the alternate theories that modify gravity are unlikely to be right; they all monkey with the overall dynamics of the universe in a way that messes up the correspondence with other cosmological observations, so they then have to make other ad hoc assumptions to fix things up. I admit I am not very up to date in this area, so there may be recent developments that I'm not aware of; but that's my understanding of where things stand.)
Q-reeus
#108
Mar2-12, 01:17 PM
P: 1,115
Peter, appreciate that in #105 you have tackled in your own inimitable style the specifics I raised earlier. There is a sense of deja vu to it all. Collectively we have created a a lengthy record of exchange for any looking on to make their minds up from. Guess you can figure what I'm saying. I will end my participation with a slightly edited cut-n-paste from #57 which turned out to be just intermission. End of the show here for me, and I trust no hard feelings between us: From #57:
Peter, thanks for your clarification and with that I agree with [some of] the above. On the broader picture, while I respect you are an accomplished master of GR maths and it's application, sad to say there is no final consensus. Bravo though for putting in a lot of effort in trying to evaporate my scepticism. At the least it has given me a clearer understanding on how this issue is seen by the GR community. Have a nice day.


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