I will talk about my recent work (arxiv: 1808.02415)  which shows that, there exists a constant $R(\gamma_0)\ge 2$, depending on the fixed weight exponent $\gamma_0>1$ in the weighted energy norm,  such that  if the norm of the data are sufficiently small on ${\mathbb R}^3\ B_R$ with the fixed number $R\ge R(\gamma_0)$, the solution exists and is unique in the entire exterior of a schwarzschild cone initiated from {|x|=R} (including the boundary) with small negative mass $−M_0$.  $M_0$ is determined according to the size of the initial data.

The application of our method  gives the exterior stability result for Einstein (massive and massless) scalar fields, which confirms  the solution converges to a small static solution, stable in the entire exterior of a schwarzschild cone with positive mass, which then is patchable to the interior results.