ADM mass for C 0 C^{0} metrics and distortion under Ricci–DeTurck flow

Abstract

We show that there exists a quantity, depending only on C 0 C^{0} data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the C 0 C^{0} sense and has nonnegative scalar curvature in the sense of Ricci flow. Moreover, the C 0 C^{0} mass at infinity is independent of choice of C 0 C^{0} -asymptotically flat coordinate chart, and the C 0 C^{0} local mass has controlled distortion under Ricci–DeTurck flow when coupled with a suitably evolving test function.