Non-local quantum gravity terms in the asymptotic 1/r expansion of static, spherically symmetric spacetimes

Determine how the non-local terms in the gravitational effective action induced by massless graviton loops in the effective field theory of general relativity contribute to the large‑radius asymptotic inverse‑power‑of‑r expansion of the static, spherically symmetric metric functions h(r) and f(r), specifying their precise structure, fixed numerical coefficients, and the orders at which they appear.

Background

The paper develops a derivative expansion of the gravitational action and analyzes corrections to static, spherically symmetric spacetimes, deliberately avoiding field redefinitions to keep all higher-derivative effects in the metric sector. Within this local operator framework, the authors compute both Yukawa-type massive contributions and the power-law 1/r expansion of the metric functions, identifying the post-Newtonian orders at which different local higher-derivative terms contribute.

They caution that assuming locality overlooks non-local contributions expected in the effective field theory of general relativity due to the massless graviton. These non-local terms come with fixed numerical coefficients and are not associated with new coupling constants. The authors explicitly state that it is not well understood how such non-local terms would enter the asymptotic expansion they derive, and emphasize the importance of including them to pin down the leading quantum-predicted deviations from general relativity.