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arXiv · 1902.02284

On the evolution of the spacetime Bartnik mass

Stephen McCormick·Pengzi Miao
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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.

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Stephen McCormick, Pengzi Miao. 2019-02-06. On the evolution of the spacetime Bartnik mass. https://arxiv.org/abs/1902.02284

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