General Relativity – Role of Gravitons in Quantum Gravity

Question

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)

Answer 1

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it was first considered by Suraj N Gupta in a paper published in 1954, and also treated by Robert Kraichnan in an unpublished batchelor's thesis at MIT.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.