During the Spring 2019 Semester, a weekly seminar will be held on General Relativity. The seminar will take place at on Thursdays at 3:00pm in Science Center 411.
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)  Title: The Anomaly flow over Riemann surfaces
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. 
10/31/2018  Alex Lupsasca (Harvard)  Title: Polarization Whorls from M87 at the Event Horizon Telescope
Abstract: The Event Horizon Telescope (EHT) is expected to soon produce polarimetric images of the supermassive black hole at the center of the neighboring galaxy M87. This black hole is believed to be very rapidly spinning, within 2% of extremality. General relativity predicts that such a highspin black hole has an emergent conformal symmetry near its event horizon. In this talk, I will briefly review this symmetry and use it to derive an analytic prediction for the polarized nearhorizon emissions to be seen at the EHT. The resulting pattern is very distinctive and consists of whorls aligned with the spin. 
11/7/2018  Jordan Keller
(BHI) 
Title: Linear Stability of Higher Dimensional Schwarzschild Black Holes
Abstract: The SchwarzschildTangherlini black holes are higherdimensional generalizations of the Schwarzschild spacetimes, comprising a static, spherically symmetric family of black hole solutions to higherdimensional vacuum gravity. The physical relevance of such solutions is intimately related to their stability under gravitational perturbations. This talk will address results on the linear stability of the SchwarzschildTangherlini black holes, part of ongoing joint work with PeiKen Hung and MuTao Wang. 
11/14/2018  Niky Kamran
(McGill) 
Title: Lorentzian Einstein metrics with prescribed conformal infinity
Abstract: We prove a local wellposedness theorem for the $(n+1)$dimensional Einstein equations in Lorentzian signature, with initial data whose asymptotic geometry at infinity is similar to that antide Sitter (AdS) space and compatible boundary data prescribed at the timelike conformal boundary of spacetime. This extends the fundamental result of Friedrich on the existence of antide Sitter spacetimes in 3+1 dimensions to arbitrary spacetime dimensions, by a different approach that allows for generic smoothness and polyhomogeneity assumptions on the initial data. This is joint work with Alberto Enciso (ICMAT, Madrid). 
12/05/2018
*room G02* 
Pengzi Miao (University of Miami)  Title: Localization of the Penrose inequality and variation of quasilocal mass
Abstract: In the study of manifolds with nonnegative scalar curvature, a fundamental result is the Riemannian Positive mass theorem. If the manifold has horizon boundary, one has the Riemannian Penrose inequality. Given a compact region with boundary in these manifolds, one wants to understand how much mass or energy is localized in such a region. This question is usually referred to as the quasilocal mass problem. In this talk, we discuss an inequality on a compact manifold with nonnegative scalar curvature, which can be thought as a body surrounding horizons. Our discussion of the rigidity case of this inequality reveals an intriguing relation between two of the most important notions of quasilocal mass, the Bartnik mass and the WangYau mass. The talk is based on joint work with Siyuan Lu. 
1/31/2019
SC 232 34pm 
Shahar Hadar (Harvard University)  Title: Latetime behavior of nearextremal black holes from symmetry
Abstract: Linear perturbations of extremal black holes exhibit the Aretakis instability, in which higher derivatives of the fields grow polynomially with time along the event horizon. Nearextremal black holes display similar behavior for some time, and eventually decay exponentially through quasinormal modes. In the talk I will show that the above behaviors are dictated by the conformal symmetry of the nearhorizon region of such black holes. I will then discuss the significance of backreaction in the problem, and show how it can be simply accounted for within the nearhorizon picture. 
2/7/2019
SC 411 34pm 
PeiKen Hung (MIT)  Title: The linear stability of the Schwarzschild spacetime in the harmonic gauge: even part

2/14/2019
SC 411 34pm 
Charles Marteau (Ecole Polytechnique) 
Abstract: I will explain how the induced geometry on a null hypersurface gives rise to a particular type of structure called Carrollian geometry. The latter emerges when taking the ultrarelativistic limit of the usual pseudoRiemannian metric. This property has strong consequences on the gravitational dynamics satisfied by the extrinsic geometry of the null hypersurface and on its symmetry group. We will see how the first one can be interpreted as ultrarelativistic conservation laws while the second corresponds to the isometries of the induced Carrollian geometry. These are very general statements for any null hypersurface but I will focus all along on a physically interesting case: the null infinity of an asymptotically flat spacetime.
