数学物理研讨班：Wang-Yau quasi-local energy toward and cross an apparent horizon

中科院数学与系统科学研究院

数学研究所

学术报告

数学物理研讨班

报告人： 赵博文 博士 (北京雁栖湖应用数学研究院)

题  目：Wang-Yau quasi-local energy toward and cross an apparent horizon

时  间：2024.08.05（周一）19：00-20：00

地  点：腾讯会议：750 255 660 

摘  要：We first prove the positivity of Wang-Yau quasi-local mass in the presence of apparent horizons. We then examine the limit of the Wang-Yau quasi-local energy as the defining spacelike $2$-surface approaches an apparent horizon from outside. Assuming $C^2$ or $W^{2,1}$ isometric embedding, we find that either 1) if the horizon is not embeddable into $R^3$, the Wang-Yau quasi-local energy blows up while the optimal embedding equation does not admit a solution near the horizon or 2) if the horizon is embeddable into $R^3$, the optimal embedding equation admits a constant solution (unique up to translation) while the Wang-Yau quasi-local mass admits a finite limit that agrees with the limit of the Brown-York mass. We also propose an extension of Wang-Yau quasi-local energy inside an horizon, i.e. for surfaces with time-like mean curvature vector.