Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik. We show that, for any metric on B̄1 that is close enough to the Euclidean metric and has reflection invariant boundary data, there always exists an asymptotically flat and scalar flat static metric extension in M = ℝ3\B1 such that it satisfies Bartnik's geometric boundary condition on ∂ B1.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics