The mass of the static extension of small spheres

Abstract

We give a simple proof to the computation of ADM mass of the static extensions of small spheres in Wiygul \cite{W1, W2}. It makes use of the mass formula $m=\frac{1}{4\pi }{\int }_{\partial M}\frac{\partial V}{\partial \nu }$ for an asymptotically flat static manifold with boundary.