On the evolution of the spacetime Bartnik mass

Abstract

It is conjectured that the full (spacetime) Bartnik mass of a surface $\Sigma$ is realised as the ADM mass of some stationary asymptotically flat manifold with boundary data prescribed by $\Sigma$. Assuming this holds true for a 1-parameter family of surfaces ${\Sigma }_t$ evolving in an initial data set {with the dominant energy condition}, we compute an expression for the derivative of the Bartnik mass along these surfaces. An immediate consequence of this formula is that the Bartnik mass of ${\Sigma }_t$ is monotone non-decreasing whenever ${\Sigma }_t$ flows outward. It is our pleasure to dedicate this paper to Robert Bartnik on the occasion of his $60$th birthday.

24 pages. v2: Updated to agree with accepted version (to appear in PAMQ); remarks and comments added

References in corpus (2)

• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass