On the evolution of the spacetime bartnik mass

Stephen McCormick, Pengzi Miao

Research output: Contribution to journalArticlepeer-review


It is conjectured that the full (spacetime) Bartnik mass of a surface Σ is realised as the ADM mass of some stationary asymptotically flat manifold with boundary data prescribed by Σ. Assuming this holds true for a 1-parameter family of surfaces Σt 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 Σt is monotone non-decreasing whenever Σt flows outward.

Original languageEnglish (US)
Pages (from-to)897-920
Number of pages24
JournalPure and Applied Mathematics Quarterly
Issue number3
StatePublished - 2019


  • Initial data
  • Quasi-local mass

ASJC Scopus subject areas

  • Mathematics(all)


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