Tachyonic fields are well accepted in QED and in string theory. Gravitons, the theoretical mediators of the gravitational force, if they existed, would by definition need to propagate faster than the speed of light to exit the black hole event horizon, unlike EM radiation.
This would not violate causality as beyond the event horizon they would propagate at the speed of light. Are there any refernces for papers which allow/predict this this
There's a misunderstanding about what the black hole horizon is. Gravitons are just spacetime perturbations, gravitational wavepackets, described by Einstein's equations. Such perturbations, for the observer that has ``crossed the horizon'', propagate at the speed of light. They reach the accelerating observer beyond the horizon after infinite time, where they are, also, recognized as spacetime perturbations, therefore traveling at the speed of light.
@ Stam
We have had this discussion before.
You are ignoring two important facts about a black holes, it can grow with time- there is no infinite time or zero time here.
Binary black holes when they merge give off a lot of energy - 3 solar masses, this comes from inside the black hole
All this has been proven by the LIGO experiment.
@ Robert
How many years ago was this analysis
Since then Hawking has said black holes don't exist !?
Black holes indeed may not exist, in the sense that they can be unstable to Hawking radiation (though this expectation hasn't been proven yet)-but the classical analysis isn't invalidated by this expectation, since Hawking radiation is beyond general relativity. That's what Hawking's statement means, assuming it can be shown to be true-which isn't the case, yet, since it's not known what happens, when black holes become too small and Hawking radiation is emitted too quickly, since the quantum backreaction of the spacetime to the emission of radiation can't be calculated.
The detection of gravitational waves is based on general relativity, not on any quantum effects that, for the black holes in question, are utterly negligible, since the Hawking temperature of such black holes is negligible-that's the real issue in detecting Hawking radiation.
It's the content of the analysis that matters, not its date, nor the name of any person. That's just for the popular press.
@ Stam
You seem to have a troll that follows you on every answer and down votes everybody who disagrees with you.
I would be very gratful if you did not answer any more of my questions
@robert
Obsolete theories devised over 100 years ago have reached its use by date
Pre quantum physics is obsolete. Equations that depnd on zero and produce infinities and singularities are not quantum physics.
The LIGO team were experimentalists they did not examine any other theory than GTR they just assumed it was correct- but there are anomalies in the results which are not explained bt GTR.
@ anyone
Ah well.
It would be good to answer the question
Is it possible to have tachyons, provided they cannot breach the event horizon, and ie. slow down to light speed once they do.
Therefore not breaching causailty.
@Igor
That's helpful - but it is a question worth serious consideration.
You could start at least by raising serious objections
Just to clarify, that, while the quantum shot noise of gravitons hasn't been detected, that gravitational waves are coherent superpositions of a macroscopic number of spin 2 particles, that are massless, and are not tachyons, is a well known property of general relativity ( just like for any field theory for the corresponding particles). They aren't vector bosons, but tensor bosons, in this case. It suffices to look at the metric perturbations about any gravitational background-which do have measurable results, incidentally and are solutions of the corresponding Einstein equations. The classical dynamics of the fields, whose excitations are such particles, is described by general relativity.
The ``tree level diagrams'' (of any field theory) describe classical processes, in fact, since there isn't any integration over off-shell degrees of freedom: the fields that are involved satisfy the classical equations of motion. So while classical gravity is described by the tree level exchange of gravitons, indeed, quantum gravity isn't. But whatever it is, its classical limit is given by general relativity. And, at least for certain kinds of black hole spacetimes, solutions of Enstein's equations, in four spacetime dimensions, it is possible to say something very specific about the properties of the quantum gravitational description, whose classical limit they are.
Tachyons, once more, describe instabilities. A lot is known about the stability of black hole spacetimes, which implies that there aren't any such instabilities, in many cases; for instance: https://math.berkeley.edu/~phintz/kdsstab.pdf to appreciate what are the issues involved. There are instabilities in others: https://arxiv.org/abs/1110.2009 for example. The idea is to show that there exists a conserved quantity, so the perturbation can't decay. All these rely on perturbations about a given background, so assume general relativity, of course. And they don't have anything to do with the black hole interior, as can be understood by passing to ``tortoise coordinates''.
Just to add to the excellent answers given,string theory does not accept tachyons in the blanket manner that you have suggested.In fact the dimensional constraints that are imposed on bosonic string theory(26), superstring Theories(10) are imposed as a result of the need to eliminate tachyonic fields(which appear as ground states) from the mass spectrum of the theories.
Back to classical black hole physics:
For you to demonstrate the functionality of your model,you need to show that the velocity four vector of a massless field(described by lightlike geodesics) tranforms from the tortoise coordinates to Kruskal-Szekeres coordinates and becomes spacelike, even outside the singularity.This is probably impossible.At least in classical GR.
The most sophisticated "functional" theory that plays with quantum field theory in curved spacetimes is the one due to Hawking et. al. I must confess that I do not understand it well enough to state whether it explicitly forbids tachyonic fields.However I hold that it should simply because it is an attempt at unifying two theories that themselves require Lorentz invariance.
@Robert,
The model described is straight forward, and there are some fairly famous names on the ticket that the propagation of gravitons, depends on the field density of dark energy. The Wheeler Misner Thorne model of the black hole ( which no one on this discussion seems to go with) also describes the singularity within the black hole event horizon.
The field density of dark energy is what produces gravity in the first instance- c.f the energy density gradient (curvature) of space time described in GTR. Not many people know that, GTR actually describes an energy density gradient- which fits in with a dark energy density gradient.
Now the proposition is that the energy density gradient reaches a critical point at the event horizon etc. etc etc - the rest is obvious to anyone who isn't hooked on classical GTR.
Will explain later
A gradient isn't invariant under general coordinate transformations-so it can't have any physical meaning.
The cosmological constant does have physical meaning, because it's a constant and thus is a non-local quantity, that is invariant under coordinate transformations.
The meaning of technical terms does matter.
@ Stam,
As before,
I would be most grateful if you didn't answer any of my questions.
Many thanks in advance
The way gravitons leave the black hole is because gravitons interacts with themselves. A graviton leaving the black hole is pulled back, it generates another graviton farther from the singularity. It goes on until a graviton leaves the event horizon, then it can be free.
Because quantum gravity is based on the notions probability (in contrast with classical Einstein's gravity which is a deterministic theory) there will be a non-zero amplitude for the graviton to go faster than the speed of light. It has nothing to do whether the graviton is within a black hole event horizon or outside. So the answer is yes it is possible.
In the context of QED, we already know that there is a finite amplitude for a photon traveling faster than c. Ref. QED: the strange theory of light and matter. Princeton University Press. p. 89.
@biswajoy
Excellent answer, but light cannot exit the black hole but a graviton can
Please elaborate
The words should have definite meanings. The objects are not separable from their properties. Stars shine, ducks quack, gravitational waves obey wave equation, which determines the speed of their propagation unambiguously. Gravitons are formal quantization of those waves.
One the other hand, you use the term "graviton" as something that rolls pleasantly on your tongue. The properties of your "gravitons" are not defined, so they might be of tar, why not?
In my opinion this is an irresponsible approach.
The ``inside'' of a black hole spacetime is the set of observers that reach the singularity in finite proper time. They can send signals, electromagnetic wavepackets or metric perturbations, up to that time. But all future signals of ``inside'' observers hit the singularity-that's why they're ``lost'' to outside observers. It suffices to draw the Carter-Penrose diagram of a black hole spacetime, as presented in all textbooks on general relativity. Only the observers ``on the horizon'' can send signals that will reach the observers, that don't fall in the singularity; and at infinite proper time of these latter observers-that's how the horizon can be defined (though there is a fine-tuning necessary to achieve this).
In all cases electromagnetic waves and metric perturbations travel at the speed of light; they satisfy the wave equation, in the black hole metric, with all that implies. It's not possible, however, to destabilize only the interior of a black hole spacetime, i.e. to affect only the observers, that will reach the singularity in finite proper time. The reason, precisely, being, that wavepackets, of the interior observers, fall in the singularity in finite proper time, before they can destabilize anything. Instabilities require that a perturbation not be able to disperse fast enough. There's been a lot of rigorous results on this issue, precisely, for nstance: https://arxiv.org/abs/1412.8379 (That's why there's no point in discussing the stability of the ``interior'', whereas it does make sense to discuss the stability of the exterior, which has been done.).
It is possible to show that electromagnetic waves have definite states of polarization and metric perturbations, also, corresponding to spin 1 for the former and spin 2 for the latter. The occupation number of such waves is macroscopic, that's why they can be identified with classical superpositions of photons and gravitons respectively. These statements don't have anything to do with either quantum electrodynamics or any quantum theory of gravity, in the sense that no superpositions of configurations that do not solve the classical equations of motion is involved, since ``tree level'' information is used in both cases.However, just as quantum electrodynamics does possess classical electrodynamics as its limit, whatever a quantum theory of gravity may be, its classical limit is general relativity, so there must be a limiting case where macroscopic superpositions of gravitons are described by gravitational waves. And this has been known for decades, through the Hamiltonian formulation of general relativity, also described in all the textbooks. It's nothing new.
Incidentally: an instability of the interior, that would affect the exterior observers, means a perturbation that produces a naked singularity. Cf. https://arxiv.org/abs/gr-qc/9710068 for a review. All known ways of describing black holes and their perturbations, have their singularities ``hidden'' by event horizons, i.e. don't have naked singularities. While it does seem possible to produce naked singularities in special cases, how generic these are isn't obvious.
@Stam
Please stop answering my questions
Third request
Many thanks in advance
Private questions-``my questions''-are to be asked privately and have no place on public fora. Public fora are just that and statements that invite suppression of technical content are deplorable. Of course, in the absence of any technical knowledge, it's not surprising to see such behavior emerge-but it has nothing to do with scholarly inquiry and is, in fact, its antithesis.
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