R440, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 440室)

The Asymptotic Behavior of Solution of Jang Equation near Closed MOTS and Shape of Interior Regularization Limit

Kai-Wei Zhao (University of California, Irvine)

Abstract:

In 1981 Schoen and Yau prove spacetime positive mass theorem by reducing the problem to the time-symmetric case which they prove in 1979. One key ingredient is Jang equation. The obstacles of solutions to be entire are marginally outer trapped surfaces (MOTS). Andersson and Metzger show that closed MOTS where solutions of Jang equation blow up are stable in the sense of MOTS. The first result in this talk is that the graph of solution of Jang equation approaches exponentially to the cylinder of such closed MOTS with strong stability assumption. In addition, Schoen and Yau exploit a family of regularization equations to show the existence and other properties of Jang equation, but they focus only on the region outside MOTS. In this talk we will characterize the geometry of interior regularization limit.