Conformally-transformed metric with arbitrary mass

Abstract

Let g_ij = δ_ij + h_ij be a C² metric on 𝔼³, where h_ij is symmetric and homogeneous in r of degree -1, and such that the linear (h_ij and its derivatives) part of the curvature scalar, denoted by R_L, is non-zero. Then there exists a metric g_ij' conformally related
to g_ij such that R_L = 0. Furthermore, the metric g_ij' can have an arbitrarily set mass.