General Relativity Workshop

2023.06.02-06.03
Beijing, China

Time: June 02-03, 2023

Venue: Room N226, South Building of Academy of Mathematics and Systems Science, Chinese Academy of Science, No.55, Zhongguancun East Road

            中国科学院数学与系统科学研究院南楼N226

Organizers: Xiaoning Wu (吴小宁, AMSS, wuxn@amss.ac.cn)

                   Siyuan Ma (马思远, AMSS, siyuan.ma@amss.ac.cn, Tel: +8615910685071)

June 02

June 03

Title and abstract:

Lars Andersson (BIMSA)

Title: The gravitational spin Hall effect

Abstract: The propagation of high-frequency electromagnetic waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate, and polarization-dependent corrections at first order in wavelength modify the propagation of light in an inhomogenous medium via a spin-orbit coupling mechanism. This effect, known as the spin Hall effect of light, has been experimentally observed. In this talk I will discuss recent work which generalizes the spin Hall effect to the propagation of light and gravitational waves in inhomogenous spacetimes.

Tianwen Luo (罗天文, 清华大学)

Title: On multi-dimensional rarefaction waves

Abstract: We study the two-dimensional acoustical rarefaction waves under the irrotational assumptions. We provide a new energy estimates without loss of derivatives and give a detailed geometric description of the rarefaction wave fronts. As an application, we show that the Riemann problem is structurally stable in the regime of two families of rarefaction waves. This is a joint work with Prof. Pin Yu in Tsinghua University.

Jinxin Xue (薛金鑫，清华大学)

Title: Geodesic dynamics around blackholes

Abstract: In this talk, we will explain our work on the geodesic dynamics around blackholes related to blackhole shadows. 

We will show that KAM theorem applies to yield a gap structure on the blackhole shadow. We will also show that Arnold diffusion occurs in a perturbed Schwarzchild or Kerr background, that is orbits with large oscillation of angular momentum. Moreover, we shall show that there exist certain chaotic orbits caused by the singular behavior of the event horizon. 

Pengyu Le (乐鹏宇，BIMSA)

Title: Two applications of Minkowski lightcone to problems in conformal geometry

Abstract: We present two applications of the geometry of the Minkowski lightcone to problems in conformal geometry. One is about the conformal invariant functional inequalities on the sphere, such as the Moser-Trudinger-Onofri inequality, the sharp Sobolev inequality on the sphere etc. The other application is a proof of the effective uniformization of 2-dim sphere with the help of the Minkowski lightcone. Both make use of the isometric embedding of a conformal deformation of the round sphere into the Minkowski lightcone.

Yangang Miao (缪炎刚，南开大学)

Title：正规黑洞研究的一点进展

Abstract：介绍当今黑洞物理中黑洞的热力学和动力学现象及其关联。通过引入共形不变性，构造高维Einstein-power-Yang-Mills正规黑洞，即选择适当的Weyl因子消除黑洞中心的奇异性，得到有趣的研究结果：Weyl因子不影响黑洞热力学，但影响黑洞的动力学性质。例如，霍金温度、熵、热熔和二阶相变都与Weyl因子无关，但是标量场扰动的似正则模却依赖于Weyl因子。特别是似正则模虚部的演化趋势反映出二阶相变点的位置与Weyl因子的形式无关，这是黑洞动力学和热力学之间新的关联方式。这个现象或许反映了共形引力黑洞的独特量子行为。

Jian Ye (叶剑，中科院数学所)

Title: On vacuum static spaces

Abstract: In this talk, we will discuss vacuum static spaces. We firstly introduce recent development of vacuum static spaces. Then we present several results on closed vacuum static spaces.

He Mei (梅河, 北京大学）

Title: Formation of black holes for Einstein equations with a positive cosmological constant

Abstract: We talk about problems related to the positive cosmological constant, especially the formation of black holes for Einstein equations.

Qian Chen (陈前，中国科学院大学)

Tilte: Nonlinear dynamics of hot, cold and bald EMs black holes in AdS spacetime 

Abstract: In this talk, I will introduce three instabilities of RN-AdS black holes (superradiant instability, near-horizon instability and nonlinear instability), which can trigger a dynamical transition to a hairy black hole. In particular, for the case of nonlinear instability, the RN-AdS black hole is in a local ground state. In order to trigger a dynamcial transition to another local ground state (hot hairy black hole), a sufficiently strong quench is required to move the system across an excited state (cold hairy black hole). On the other hand, the real-time dynamics from the excited state to the two local ground states are also revealed.