Spherically symmetric static solutions in a non-local infrared modification of General Relativity

Abstract

We discuss static spherically symmetric solutions in a recently proposed non-local infrared modification of Einstein equations induced by a term $m^2{g}_{\mu \nu }{\square }^{-1}R$, where $m$ is a mass scale. We find that, contrary to what happens in usual theories of massive gravity, in this non-local theory there is no vDVZ discontinuity and classical non-linearities do not become large below a Vainshtein radius parametrically larger than the Schwarzschild radius $r_S$. Rather on the contrary, in the regime $r\ll m^{-1}$ the corrections to the metric generated by a static body in GR are of the form $1+\mathcal{O}(m^2{r}^2)$ and become smaller and smaller toward smaller values of $r$. The modification to the GR solutions only show up at $r>m^{-1}$. For $m=\mathcal{O}(H_0)$, as required for having interesting cosmological consequences, the non-local theory therefore recovers all successes of GR at the solar system and lab scales.

29 pages, 5 figures. v2: expanded discussion of conceptual aspects. The version to appear in JHEP

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