2022 NCTS Workshop on Mathematical General Relativity

Registration

Mu-Tao Wang 王慕道, Columbia University

Title: Angular momentum and supertranslation in general relativity (相對論中的角動量和超平移)

Abstract: Two black holes rotate about each other and eventually merge into a single black hole. How does one measure the angular momentum carried away by gravitational radiation during this merger? This has been a subtle issue since the 1960’s due to the existence of ``supertranslation ambiguity”: the angular momentums recorded by two observers of the same system may not be the same.

In this talk, I shall describe how the theory of quasilocal mass and optimal isometric embedding identifies a new definition of angular momentum that is free of any supertranslation ambiguity. This is based on joint work with Po-Ning Chen, Jordan Keller, Ye-Kai Wang, and Shing-Tung Yau.

Lunch break

Lan-Hsuan Huang 黃藍萱, University of Connecticut

Title: A geometric boundary value problem in general relativity

Abstract: Constructing Riemannian metrics of zero scalar curvature with prescribed boundary geometry is of fundamental importance in general relativity and differential geometry. This talk will focus on a special class of metrics of zero scalar curvature, called static vacuum. A static vacuum metric produces a Ricci flat manifold of one dimension higher and is related to scalar curvature deformation and gluing. There had been very limited examples of static vacuum metrics without symmetry. For example, the celebrated Uniqueness Theorem of Static Black Holes says that any asymptotically flat, static vacuum metric with minimal surface boundary must be rotationally symmetric. In contrast, motivating by his quasi-local mass program, R. Bartnik conjectured that one should always find an asymptotically flat, static vacuum metric with quite arbitrarily prescribed boundary geometry. I will discuss recent progress toward this conjecture. It is based on joint work with Zhongshan An.

Tea break

Po-Ning Chen 陳泊寧, University of California, Riverside

Title: Conserved quantities in general relativity, from quasi-local to null infinity

Abstract: Energy and angular momentum are of fundamental importance. However, there have been great difficulties to find physically acceptable definitions of these concepts in general relativity since Einstein's time. Indeed, there is no density for gravitational energy in general relativity due to Einstein's equivalence principle.

In this talk, I shall describe the theory of quasilocal conserved quantities based on the Hamilton-Jacobi approach and how it leads to a new definition of conserved quantities, including angular momentum and center of mass at null infinity. This is based on joint work with Jordan Keller, Mu-Tao Wang, Ye-Kai Wang, and Shing-Tung Yau.