数学研究所
学术报告
广义相对论研讨班
Speaker: 韩青 教授 (美国Notre Dame大学）
Inviter: 吴小宁 研究员
Language: English
Title: The Mass-Angular Momentum Inequality for Multiple Black Holes
Time&Venue: 2025年5月17日（星期六） 9:00-10:00&南楼N226
Abstract: This is the second in a series of two papers to establish the conjectured mass-angular momentum inequality for multiple black holes, modulo the extreme black hole 'no hair theorem'. More precisely it is shown that either there is a counterexample to black hole uniqueness, in the form of a regular axisymmetric stationary vacuum spacetime with an asymptotically flat end and multiple degenerate horizons which is 'ADM minimizing', or the following statement holds. Complete, simply connected, maximal initial data sets for the Einstein equations with multiple ends that are either asymptotically flat or asymptotically cylindrical, admit an ADM mass lower bound given by the square root of total angular momentum, under the assumption of nonnegative energy density and axisymmetry. Moreover, equality is achieved in the mass lower bound only for a constant time slice of an extreme Kerr spacetime. The proof is based on a novel flow of singular harmonic maps with hyperbolic plane target, under which the renormalized harmonic map energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solutions to the harmonic map equations and their linearization.
Speaker: 张一岳 (北京雁栖湖应用数学研究中心）
Inviter: 吴小宁 研究员
Language: Chinese
Title: Initial data sets with vanishing mass are contained in pp-wave spacetimes
Time&Venue: 2025年5月17日（星期六） 10:30-11:30&南楼N226
Abstract: In 1981, Schoen-Yau and Witten showed that in General Relativity both the total energy E and the total mass m of an initial data set modelling an isolated gravitational system are non-negative. Moreover, if E=0, the initial data set must be contained in Minkowski space. In this paper, we show that if m=0, i.e. if E equals the total momentum |P|, the initial data set must be contained in a pp-wave spacetime. Our proof combines spinorial methods with spacetime harmonic functions and works in all dimensions. Additionally, we find the decay rate threshold where the embedding has to be within Minkowski space and construct non-vacuum initial data sets with m=0 in the borderline case. As a consequence, this completely settles the rigidity of the spacetime positive mass theorem for spin manifolds.
Speaker: Prof. Piotr T. Chrusciel
（北京雁栖湖应用数学中心）
Inviter: 吴小宁 研究员
Language: English
Title:Who is afraid of a negative lapse ?
Time&Venue: 2025年5月17日（星期六） 14:00-15:00&南楼N226
Abstract: I will discuss the properties of the Anderson-York equations, where one can prescribe arbitrarily the shift vector and a densitised lapse. This talk is based on joint work with Bobby Beig.
Speaker: 何孝凯 教授 （湖南第一师范）
Inviter: 吴小宁 研究员
Language: Chinese
Title:Bondi Mass, Memory Effect and Balance Law of Polyhomogeneous Spacetime
Time&Venue: 2025年5月17日（星期六） 9:00-10:00&南楼N226
Abstract: Spacetimes with metrics admitting an expansion in terms of a combination of powers of 1/r and ln r are known as polyhomogeneous spacetimes. The asymptotic behaviour of the Newman-Penrose quantities for these spacetimes is presented under certain gauges. The Bondi mass is revisited via the Iyer-Wald formalism. The memory effect of the gravitational radiation in the polyhomogeneous spacetimes is also discussed. It is found that the appearance of the logarithmic terms does not affect the balance law and it remains unchanged as the one of spacetimes with metrics admitting an expansion in terms of powers of 1/r.
