Can flat spacetime model Black Holes?

waterfall

I'm asking because some of you state that flat spacetime can't model black holes... meaning even between the planck scale and event horizon, but yet atyy said spin-2 field in flat spacetime is equivalent to General Relativity for spacetime that is covered by harmonic coordinates which atyy thought can include the event horizon up to the planck scale. So this means spin-2 field in flat spacetime can model black holes.

So can flat spacetime model black holes or not? And if you add spin-2, why can it do that?
Why, is there flat spacetime without spin-2 field? Are these distinct concepts?

bcrowell

MTW has a discussion of this on p. 425. They give a final interpretation by Deser, with a reference to Deser, S., 1970, "Self-interaction and gauge invariance," Gen Rel and Grav 1, 9. They describe an interative process in which flat-spacetime gravity, which is not mathematically self-consistent, is repaired. After an infinite process of iteration, we arrive at a theory in which the original flat spacetime "is no longer observable." They claim that the resulting theory makes the same predictions as GR.

Mentz114 linked to a review article by Baryshev that is more up to date than MTW: http://arxiv.org/abs/gr-qc/9912003 . Baryshev says that the two approaches are not in fact equivalent, so "field-theory gravity" (FTG) is not equivalent to GR as claimed by MTW.

Some quotes from the Baryshev paper:

"In fact, Deser showed no more then it is possible to find such an expression of EMT which at
the third iteration gives Einstein equations and in no way this leads to the conclusion about identity
of field and geometrical approaches, as was claimed in the book of Misner, Thorne, Weeler (1977).
Moreover, the essence of field approach suggests such a choice of gravitational EMT that satisfies zero
trace (massless graviton) and positive energy density of gravitational field and namely these properties
should be tested first. Deser’s EMT does not satisfy these conditions. It is easy to demonstrate that
positive energy requirement leads to radical difference of field approach from that of geometrical one
(see 5.3)."

"[...]black holes are prohibited [in FTG] by the energy conservation" (5.3)

"Frequently
one finds in literature that black holes have already been detected, because there are systems with
components more massive than the Oppenheimer-Volkoff limit, i.e. over the three solar masses. This
statement is not correct, since this limit exists only in GR, but in FTG there could exist relativistic
stars with larger masses."

What I'm unable to gauge at this point is whether Baryshev's interpretation is controversial, or whether everyone in the field now agrees that Deser's conclusion about the equivalence of the two theories was incorrect. A shortcut method for checking into this without digging deep into the math is to see whether Baryshev's review paper was published in a refereed journal (apparently not) and whether Baryshev publishes regularly in the usual journals where relativists publish (looks like the answer is no, after a quick dig through arxiv and Baryshev's web site). So I would be cautious about assuming that Baryshev is correct and/or noncontroversial.

waterfall

You mentioned the original flat spacetime "is no longer observable". You are saying that the spin-2 fields can act on the flat spacetime and also model black holes? This is the same as saying that flat spacetime can also model black holes in contrast to what some of you believe that it can't.. that only General Relativity can model black holes. The fact is Flat spacetime with spin-2 fields can too. Anyone objects to this?

Do you happen to know the meaning of Harmonic Coordinates? Is it valid in between the event horizon and the boundary of the planck scale singularity?

waterfall

Thanks the above kind of paper is what I'm looking for. So in strong fields, flat spacetime with spin 2 fields can't model such things like Black Holes. Now the reason I'm asking is because I'd like to know whether a quantum theory of gravity.. or quantum gravity can produce the degrees of freedom where the spin-2 versions in flat spacetime can model strong fields too. I mean quantum gravity is supposed to address beyond planck scale. But how about strong fields like between the event horizon and the boundary of the planck scale. Can a quantum gravity theory enable spin-2 over flat spacetime in strong fields such as between event horizons and near planck scale too in contrast to normal Field Theory of Gravitation? This is my main question.

bcrowell

Another paper along these lines: T.Padmanabhan, "From Gravitons to Gravity: Myths and Reality," http://arxiv.org/abs/gr-qc/0409089

waterfall

In the paper you quoted earlier. It is concluded that "It is quite natural that fundamental description of gravity will be found on quantum level and geometrical description of gravity may be considered as the classical limit of quantum relativistic gravity theory".

My question is. Can a quantum theory of gravity.. or quantum gravity produce the degrees of freedom where the spin-2 versions in flat spacetime can model strong fields too. I mean quantum gravity is supposed to address beyond planck scale. But how about strong fields like between the event horizon and the boundary of the planck scale. Can a quantum gravity theory enable spin-2 over flat spacetime in strong fields such as between event horizons and near planck scale too in contrast to normal Field Theory of Gravitation??

atyy

@bcrowell: as an argument from authority, harmonic coodinates are used in the proof of local existence of solutions to the EFE. I believe the restriction to "local" is due to the generic development of singularities, which the field on flat spacetime approach obviously cannot cover. The field on flat spacetime approach also cannot cover exotic topologies. OTOH, I think the ADM formalism, which is as far as we know good enough for observable physics, also assumes nice topologies. I am, however, not sure whether the conditions to use ADM and field theory on flat spacetime are exactly equivalent.

Will's review (Eqn 62) references MTW for the EFE written using flat spacetime, and says "Equation (62) is exact, and depends only on the assumption that spacetime can be covered by harmonic coordinates."

Weinberg's text (chapter 8) displays harmonic coordinates for the Schwarzschild and FRW solutions (obviously restricted to the parts with nice topologices).

bcrowell

I don't claim to know more than epsilon about this highly technical topic within GR. One thing that strikes me, simply from casually skimming some of the papers, is that Baryshev seems to be making some very strong claims, from which Padmanabhan carefully abstains.

Another observation is that Baryshev's section 5.3 seems to be claiming not just that black-hole singularities can't form in what he calls "FTG," but also that event horizons can't form. It wouldn't surprise me (although I don't find it obvious as atyy does) if spin-2 on a flat background can't produce singularities (what if the field blows up...?). But saying that it forbids event horizons seems extremely provocative. And Baryshev's argument smells fishy to me. He says:

"Eddington in his famous discussion with Chandrasekhar about the fate of white dwarfs with masses over the critical one, stated that there should be the law of nature preventing the contraction of massive stars under their gravitational radius.
It is easy to show that there is such a law in FTG and it is the law of conservation of energy!"

Huh!? There is no law of conservation of energy in GR. Maybe he's saying that there is one in what he calls FTG?

Passionflower

Perhaps I missed that discussion all I think is that Eddington treated Chandrasekhar in a despicable and unforgivable way.

atyy

Here are some thoughts. Black holes formulated as event horizons are defined non-locally in spacetime. Harmonic coordinates can penetrate the event horizon. However, I don't know if harmonic coordinates cover enough of black hole spacetimes that a non-local structure like an event horizon can also be defined. The non-local nature of an event horizon also makes them hard to see in numerical relativity, so people have developed other related, but quasilocal sorts of horizons.

The restriction of gravity as a field on flat spacetime to less than Planck scale curvature comes from thinking of it as an effective quantum field theory, not as a classical field theory. If I understand correctly, gravity as an effective quantum field theory is a working quantum theory of gravity for all phenomena thus far observed. This theory does not make sense near the Planck scale, so it can't have singularities, since the theory doesn't even exist once the curvature approaches Planck scale.

I guess the important question is whether Hawking radiation can be seen in harmonic coordinates.

waterfall

So does anyone know if harmonic coordinates can "cover enough of black hole spacetimes that a non-local structure like an event horizon can also be defined"?

If yes, then spin 2 field on flat spacetime can cover black hole event horizon too down to near planck scale.

If no, then spin 2 field on flat spacetime as effective quantum field theory of gravity can't cover black hole event horizon.

Now my question is. If no. Would the right or complete quantum gravity theory be able to cover event horizon NOT covered by harmonic coordinates? How?

This is what I wanted to know for weeks but can't verbalize. Hope someone can clarify all these basic questions first. Thanks.

waterfall

While waiting the answers to the above I have some rudamentary questions:

1. In the statement "Black holes formulated as event horizons are defined non-locally in spacetime.". So the "non-locally" is also true in spin-2 flat spacetime. Now I wonder if this is related to quantum non-locality. That is. Can one model event horizon in flat spacetime (in case these are not covered by harmonic coordinates) by using some kind of quantum non-locality thing (in quantum gravity where quantum and GR is united)?

2. In low energy where spin-2 flat spacetime works. How do you calculate how to scatter a graviton with an electron? I haven't seen much calculations about this.

3. How do you define or address Background Independence (no prior geometry) in spin-2 flat spacetime?

harrylin

"black hole" is a bit vague of a concept. More precisely, do you want it to predict for example Hawking radiation? It has not been observed, so are sure that you want it?

bcrowell

Why did we suddenly start talking about quantum mechanics? As far as I understand, this entire question is purely classical, and all the papers we've been discussing are purely classical.

waterfall

What classical? atyy said in message #10 that "The restriction of gravity as a field on flat spacetime to less than Planck scale curvature comes from thinking of it as an effective quantum field theory, not as a classical field theory."

About quantum mechanics. He said in the same message that "Black holes formulated as event horizons are defined non-locally in spacetime". Here since spin-2 field on flat spacetime has difficulty with event horizons because of their non-local nature. Then why not tie it up to quantum non-locality. Who knows, they may have similar mechanisms or related. Why not?