I Geometry of GR v. Spin-2 Massless Graviton Interpretation

[ohwilleke]

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).

 

[Demystifier]

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.

 

[Urs Schreiber]

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.