# General Relativity Seminar

During the Fall 2018 Semester, a weekly seminar will be held on General Relativity. The seminar will take place at on Wednesdays at 11:00am in CMSA G02.

The schedule will be updated below.

 Date Speaker Title/abstract 9/7/2018 Christos Mantoulidis (MIT) Title: Capacity and quasi-local mass Abstract. This talk is based on work with P. Miao and L.-F. Tam. We derive new inequalities between the boundary capacity of an asymptotically flat 3-manifold with nonnegative scalar curvature and boundary quantities that relate to quasi-local mass; one relates to Brown-York mass and the other is new. Among other things, our work yields new variational characterizations of Riemannian Schwarzschild manifolds and new comparison results for surfaces in them. 9/12/2018 Aghil Alaee (CMSA) Title:  Mass-angular momentum inequality for black holes Abstract:  In this talk, I will review the results of mass-angular momentum inequality for four-dimensional axisymmetric black holes. Then I will establish versions of this inequality for five-dimensional black holes and in particular black ring, which is the most intriguing asymptotically flat solution of vacuum Einstein equations. Moreover, I will show these inequalities are sharp if and only if the initial data sets are isometric to the canonical slices of known extreme stationary solutions. These results are joint work with Marcus Khuri and Hari Kunduri. 9/19/2018 Pei-Ken Hung (MIT) Title: The linear stability of the Schwarzschild spacetime in the harmonic gauge: odd part Abstract: We study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of Regge-Wheeler quantities, we are able to estimate the odd part of Lichnerowicz d’Alembertian equation. In particular, we prove the solution decays at rate $\tau^{-1+\delta}$ to a linearlized Kerr solution. 9/26/2018 Jordan Keller (BHI) Title: Quasi-local Angular Momentum and Center-of-Mass at Future Null Infinity Abstract: We calculate the limits of the quasi-local angular momentum and center-of-mass defined by Chen-Wang-Yau [3] for a family of spacelike two-spheres approaching future null infinity in an asymptotically flat spacetime admitting a Bondi-Sachs expansion.   Our result complements earlier work of Chen-Wang-Yau [2], where the authors calculate the quasi-local energy and linear momentum at null infinity. Finiteness of the quasi-local center-of-mass requires that the spacetime be in the so-called center-of-mass frame, which amounts to a mild assumption on the mass aspect function corresponding to vanishing of the quasi-local linear momentum calculated in [2].  With this condition and the assumption that the mass aspect function is non-trivial, we obtain explicit expressions for the quasi-local angular momentum and center-of-mass at future null infinity in terms of the observables appearing in the Bondi-Sachs expansion of the spacetime metric. This is joint work with Ye-Kai Wang and Shing-Tung Yau. 10/3/2018 Christos Mantoulidis (MIT) Title: The Bartnik mass of apparent horizons Abstract: We will discuss a spectral characterization of apparent horizons in three-dimensional time-symmetric initial data sets. Then, for a dense class of nondegenerate apparent horizons, we will construct sharp asymptotically flat extensions to conclude that their Bartnik mass equals their Hawking mass. This is joint work with R. Schoen. 10/10/2018 Salem Al Mosleh (CMSA) Title: Thin elastic shells and isometric embedding of surfaces in three-dimensional Euclidean space Abstract: We will first discuss the reduction of theories describing elastic bodies in three-dimensions to effective descriptions defined on embedded surfaces. Then, we describe the isometric deformations of surfaces and the key role of played by asymptotic curves, curves with zero normal curvature, in determining the local mechanical behavior of thin shells. This was joint work with C. Santangelo. 10/17/2018 Sébastien Picard (Harvard) Abstract: The Anomaly flow is a geometric flow on Calabi-Yau threefolds which is motivated by string theory. We will study the flow on certain fibrations where it reduces to a scalar evolution equation on a Riemann surface. This is joint work with T. Fei and Z. Huang.