Geometry of GR v. Spin-2 Massless Graviton Interpretation

In summary, gravitons are perturbations of the metric tensor that arise from the interaction of gravitons with other particles in a flat Minkowski space-time. The topology of space-time in graviton theory is not fixed, and depends on the particular classical solution that is chosen.
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ohwilleke
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In classical general relativity, gravity is simply a curvature of space-time.

But, a quantum field theory for a massless spin-2 graviton has as its classical limit, general relativity.

My question is about the topology of space-time in the hypothetical quantum field theory of a massless spin-2 graviton ("graviton theory").

In graviton theory, do all of the phenomena associated with the curvature of space-time in GR arise from gravitons interacting with gravitons and other particles in a "flat" Minkowski space-time in common with the space-time of the Standard Model, or does space-time have some other topology in graviton theory? Is there any published academic literature definitively resolving the question one way or the other?

(Apparently, this question was previously addressed in this thread: https://www.physicsforums.com/threads/gravitons-spacetime-curvature-geometry.129300/) eleven years ago, but the short discussion in that thread is a bit disjointed and hard to follow).
 
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Gravitons are perturbative objects. Spacetime topology is a non-perturbative aspect of gravity. Therefore gravitons cannot contain all information about gravity. This is like trying to understand quark confinement from Feynman diagrams in QCD.
 
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Just to amplify what H. Nikolic just said:

Given any time-orientable globally hyperbolic spacetime (it need not be Minowski spacetime, could also be a Schwarzschild for instance), the linearization of the Einstein equations around that solution to first order yields the wave equation for the components of the perturbations of the metric tensor; and quantizing these first order free field perturbations of the metric yields the field whose quanta are gravitons. So by definition gravitons are (quanta of) tiny fluctuations of the metric tensor around a given classical solution. In particular the underlying spacetime manifold and its topology is fixed background structure for the definition of gravitons.

Literature on the perturbative quantum gravity "of gravitons", if you wish, is listed here.
 
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1. What is the Geometry of GR v. Spin-2 Massless Graviton Interpretation?

The Geometry of GR v. Spin-2 Massless Graviton Interpretation is a theoretical framework in which the principles of General Relativity (GR) and the concept of a massless spin-2 graviton are combined to understand the behavior of gravity at a quantum level.

2. How does this interpretation differ from the traditional understanding of gravity?

This interpretation differs from the traditional understanding of gravity because it incorporates the concept of a massless spin-2 graviton, which is a fundamental particle that mediates the force of gravity between masses. This is in contrast to GR, which describes gravity as a curvature of spacetime.

3. What are the implications of this interpretation for the understanding of the universe?

This interpretation has significant implications for our understanding of the universe, as it allows for a more complete understanding of gravity at a quantum level. It also has the potential to reconcile the theories of GR and quantum mechanics, which is a major goal in modern physics.

4. How is this interpretation supported by experimental evidence?

While there is currently no direct experimental evidence for the existence of a massless spin-2 graviton, this interpretation is supported by theoretical calculations and fits well with the known behavior of gravity. Additionally, experiments such as the detection of gravitational waves provide indirect evidence for the existence of gravitons.

5. Are there any potential challenges or criticisms of this interpretation?

As with any scientific theory, there are potential challenges and criticisms of this interpretation. Some physicists argue that the concept of a massless spin-2 graviton is not well-defined and may not be compatible with other fundamental theories. Additionally, there is currently no way to directly test the existence of gravitons, which makes it difficult to fully confirm this interpretation.

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