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First I want to say that I am a layperson, so I want intuitive answers.

So all the 3 fundamental forces in nature has a carrier particle except gravity. So we have hypothesized the existence of graviton. But I want to know that how does the concept of graviton relates to the concepts of general relativity which describes gravity as the curvature of space-time.

So here are the Questions:-

$(1)$ Are gravitons consistent with the concept of curvature of space-time?

$(2)$ If the answer to $(1)$ is 'yes' then how does it account for gravitational waves which described as wobbling of space-time?

And if the answer to $(1)$ is 'no' then how does gravitons relate to curvature of space-time?

$(3)$ Blackholes are defined as an extremely curved region of spacetime with a singularity or a ring-singularity in the middle. So how does gravitons explain blackholes and singularities?

(If this question is poorly framed then I am sorry, I cannot clarify more than this)

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    $\begingroup$ What does your question (1) even mean? What does it mean to "reject the curvature of space-time"? The honest answer to (3) is "we don't know". $\endgroup$ – Prahar Mitra Apr 17 at 8:19
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    $\begingroup$ @Prahar Mitra. What I meant by question $(1)$ is : Does the gravitons explain gravity without the need of curved spacetime? $\endgroup$ – Ranjit Kumar Sarkar Apr 17 at 9:30
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    $\begingroup$ Of course not. Gravitons are a consequence of quantizing general relativity (to the extent that that's possible). They do not get rid of curved spacetime at all. Rather, they emerge from it. $\endgroup$ – Prahar Mitra Apr 17 at 9:31
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Gravitons are theorised by looking at the linearisation of a perturbation of curved spacetime and it turns out that it is a massless spin-2 particle. Hence as one commenter has pointed out, it presupposes curved spacetime.

However, having derived the graviton in curved space, we can consider it in flat space. According to Feynmans Lectures on Gravitation, if we also linearly couple the graviton to the energy-momentum tensor the full set of Einsteins field equations can be derived. Hence, the underlying space that we took to be flat, is in fact curved. Thos is entirely unexpected. In fact, Feynman writes in section 8.4:

The fact is, that a spin-2 field has this geometrical interpretation; this is not something readily explainable - it is just marvellous.

This argument did not originate with Feynman. As the introduction to the book makes clear, it was first considered by Suraj N Gupta in a paper published in 1954, and also treated by Robert Kraichnan in an unpublished batchelor's thesis at MIT. However, Feynman's derivation was independent of this earlier work.

A different argument was given by Weinberg in the mid-60s,who assuming 'reasonable analycity' properties of graviton-graviton scatterings, showed that the graviton could only be Lorentz invariant if and only if it couples to matter and itself universally, that is the strong equivalence principle is satisfied. From there, the rest of GR can be derived.

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  • $\begingroup$ Ok, that is quite rough for a layman to read. I know because I'm also a layman. $\endgroup$ – Askar Kalykov Apr 17 at 18:39
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    $\begingroup$ @Askar Kalyov: This is a physics site so some familarity wirh physical concepts can be assumed. It's not what I would write if I was in front of an audience of, say, poets. $\endgroup$ – Mozibur Ullah Apr 17 at 20:56
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    $\begingroup$ @AskarKaylov This site is open to questions about physics at any level. $\endgroup$ – my2cts Apr 18 at 13:24
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These are all fine questions, but it is important to get first a proper intuition.

Gravitons are to gravity what photons are to electromagnetic field, or what phonons (quasi-particles of sound) are to deformation. They are all excitations of some field (quantum field, to be precise). "Excitation" implies there is some default state of the field, which we imagine to be somehow "perturbed". We call the default state "vacuum" and perturbations - "particles" (because when there are few of them, they behave like regular particles). What constitutes a "vacuum" and what a "particle" is quite subjective, and some choices are better than others. We try to pick vacuum as a stationarry and most "calm" state of the field (uncertainty principle makes it impossible for the field to be completely calm). Classical stationary solutions to Einstein equations is a good "seed" for the vacuum of gravitational field.

Given the intuition, we imagine gravitons being superimposed onto the background of some quasi-stationary curved space-time. When gravitons act synchronously, we call it gravitational waves (in the same way as we call synchronized movement of photons as electromagnetic waves). Gravitons do not explain black holes, they are just quants of perturbations on the curved background.

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  • $\begingroup$ "Gravitons are to gravity what photons are to electromagnetic field" in a quantum gravity theory that doe snot yet exist. $\endgroup$ – my2cts Apr 17 at 13:33
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    $\begingroup$ We have though linearized quantum gravity in curved spacetime. It is quite sufficient for many purposes. $\endgroup$ – Pavlo. B. Apr 17 at 15:23
  • $\begingroup$ Can you give a reference? There is not even mention of this on wikipedia. I could only find this: authors.library.caltech.edu/72875/1/PhysRev.113.745.pdf. $\endgroup$ – my2cts Apr 17 at 16:32
  • $\begingroup$ Sorry, I cannot. I assumed I can (wiki discusses non-renormalizability of gravity), but I don't find anything easily either. But I am pretty sure quantum mechanics of linear deviation of gravitational field from a stationary solution is a thing. You would linearize Einstein's equations, find normal oscillatory modes and make each of them into a corresponding quantum oscillator. Increasing the energy of each oscillator you would verbally equate with "adding a graviton". $\endgroup$ – Pavlo. B. Apr 17 at 16:56
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    $\begingroup$ @my2cts Here's one: Introduction to the Effective Field Theory Description of Gravity, arXiv:gr-qc/9512024 $\endgroup$ – Chiral Anomaly Apr 18 at 3:21
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We don't have a quantum theory of gravity yet, so the honest answer to your questions is "nobody knows". But I think most people would guess that the quantum theory of gravity would bear a similar relationship to curved spacetime as the quantum theory of electrodynamics (QED) bears to Maxwell's picture of electric and magnetic fields. That is, spacetime would "appear" to be curved at large scales, but the underlying mathematical picture would be very different -- just as the mathematical description of quantum electrodynamics is very different from Maxwell's equations. On the other hand working engineers use Maxwell's equations every day, as they're a very good approximation; similarly, Einstein's field equations are going to be a very good approximation of whatever final theory of gravity there is.

Gravitational waves are probably explained as a collection of gravitons, just as electromagnetic waves are explained in QED as a collection of photons.

Black holes would still be described as "a region of spacetime which light cannot escape from", but the quantum explanation would be in terms of the strength of exchange of virtual gravitons rather than the extreme curvature of spacetime.

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