CMSA General Relativity Seminar: Improvability of the dominant energy scalar and Bartnik’s stationary conjecture
CMSA GENERAL RELATIVITY SEMINAR
Lan-Hsuan Huang - University of Connecticut
In this talk, we will introduce the concept of improvabilty of the dominant energy scalar and discuss strong consequences of non-improvability. We employ new, large families of deformations of the modified Einstein constraint operator and show that, generically, their adjoint linearizations are either injective, or else one can prove that kernel elements satisfy a "null-vector equation''. Combined with a conformal argument, we make significant progress toward Bartnik's stationary conjecture. More specifically, we prove that a Bartnik minimizing initial data set can be developed into a spacetime that both satisfies the dominant energy condition and carries a global Killing field. We also show that this spacetime is vacuum near spatial infinity. This talk is based on the joint work with Dan Lee.