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 quasilocal 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 3manifold with nonnegative scalar curvature and boundary quantities that relate to quasilocal mass; one relates to BrownYork 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: Massangular momentum inequality for black holes
Abstract: In this talk, I will review the results of massangular momentum inequality for fourdimensional axisymmetric black holes. Then I will establish versions of this inequality for fivedimensional 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  PeiKen 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 ReggeWheeler 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: Quasilocal Angular Momentum and CenterofMass at Future Null Infinity
Abstract: We calculate the limits of the quasilocal angular momentum and centerofmass defined by ChenWangYau [3] for a family of spacelike twospheres approaching future null infinity in an asymptotically flat spacetime admitting a BondiSachs expansion. Our result complements earlier work of ChenWangYau [2], where the authors calculate the quasilocal energy and linear momentum at null infinity. Finiteness of the quasilocal centerofmass requires that the spacetime be in the socalled centerofmass frame, which amounts to a mild assumption on the mass aspect function corresponding to vanishing of the quasilocal linear momentum calculated in [2]. With this condition and the assumption that the mass aspect function is nontrivial, we obtain explicit expressions for the quasilocal angular momentum and centerofmass at future null infinity in terms of the observables appearing in the BondiSachs expansion of the spacetime metric. This is joint work with YeKai Wang and ShingTung 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 threedimensional timesymmetric 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 threedimensional Euclidean space
Abstract: We will first discuss the reduction of theories describing elastic bodies in threedimensions 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 CalabiYau 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.
