Uniqueness of the Reissner-Nordstrom metric near the null infinity

In the Newman-Penrose formalism,we prove that the Reissner-Nordstrom metric is the only asymptotically fat,static,axially symmetric,Petrov type-D analytic solution of the electro-vacuum Einstein-Maxwell equations near the null infinity.

On the angular momentum of compact binary coalescence

The supertranslation ambiguity issue of angular momentum is a long-standing problem in general relativity.Recently,there appeared the first definition of angular momentum at null infinity that is supertranslation invariant.However,in the compact binary coalescence community,supertranslation ambiguity is often ignored.This paper demonstrates that we have the happy circumstance that the newly defined angular momentum coincides with the classical definition at the quadrupole level.

On limit behavior of quasi-local mass for ellipsoids at spatial infinity

We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime.These ellipsoids are not nearly round but they are of interest as an admissible parametrized foliation defining the Arnowitt–Deser–Misner mass.The Hawking mass of this family of ellipsoids tends to-∞.In contrast,we show that the Hayward mass converges to a finite value.Moreover,a positive mass type theorem is established.The limit of the mass has a uniform positive lower bound no matter how oblate these ellipsoids are.This result could be extended for asymptotically Schwarzschild manifolds.And numerical simulation in the Schwarzschild spacetime illustrates that the Hayward mass is monotonically increasing near infinity.

Hayward Quasilocal Energy of Tori

In this paper, the authors show that one cannot dream of the positivity of the Hayward energy in the general situation. They consider a scenario of a spherically symmetric constant density star matched to the Schwarzschild solution, representing momentarily static initial data. It is proved that any topological tori within the star, distorted or not,have strictly positive Hayward energy. Surprisingly we find analytic examples of ‘thin’ tori with negative Hayward energy in the outer neighborhood of the Schwarzschild horizon.These tori are swept out by rotating the standard round circles in the static coordinates but they are distorted in the isotropic coordinates. Numerical results also indicate that there exist horizontally dragged tori with strictly negative Hayward energy in the region between the boundary of the star and the Schwarzschild horizon.

非球对称情形箍猜想若干进展

本文简要地介绍了本文作者及其合作者最近几年在非球对称情形箍猜想研究方面的若干进展.