A flow approach to Bartnik’s static metric extension conjecture in axisymmetry. (English) Zbl 1437.83011
In this article, the authors developed a new approach to construct static metric extensions as they arise in R. Bartnik’s conjecture [Commun. Pure Appl. Math. 39, 661–693 (1986; Zbl 0598.53045)]. They suggested a geometric flow approach, coupled to the Weyl-Papapetrou formalism for axisymmetric static solutions to the Einstein vacuum equations. The elliptic Weyl-Papapetrou system becomes a free boundary value problem in this approach. The article is well written and will have impact to the readers.
Reviewer: P. K. Sahoo (Hyderabad)
MSC:
83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
83C15 | Exact solutions to problems in general relativity and gravitational theory |
53Z05 | Applications of differential geometry to physics |
53C20 | Global Riemannian geometry, including pinching |
58E20 | Harmonic maps, etc. |