Conditions for patching local perturbative treatments into a global spacetime

Ascertain the precise conditions under which local perturbative treatments of graviton dynamics around a background Minkowski metric can be consistently patched together to yield a global curved spacetime description, including any constraints due to manifold topology and global features.

Background

The self-interaction approach treats gravitons as perturbations about a fixed background metric, aiming for curved geometry to emerge from interactions. While Riemann normal coordinates justify local flatness approximations, extending these local treatments to a global spacetime requires compatibility conditions that depend on topology and global structure.

The authors emphasize that the criteria for when such local perturbative patches can be consistently stitched together are not established, limiting the approach’s scope beyond local regions.