Spherically symmetric static solutions in a nonlocal infrared modification of General Relativity

We discuss static spherically symmetric solutions in a recently proposed nonlocal infrared modification of Einstein equations induced by a term m2gμν □−1R, where m is a mass scale. We find that, contrary to what happens in usual theories of massive gravity, in this nonlocal theory there is no vDVZ discontinuity and classical non-linearities do not become large below a Vainshtein radius parametrically larger than the Schwarzschild radius rS . Rather on the contrary, in the regime r ≪ m−1 the corrections to the metric generated by a static body in GR are of the form 1 + O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document}(m2r2) 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 = O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document}(H0), as required for having interesting cosmological consequences, the nonlocal theory therefore recovers all successes of GR at the solar system and lab scales.