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 G10. 

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) Title: The Anomaly flow over Riemann surfaces

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.

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 high-spin 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 near-horizon 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 Schwarzschild-Tangherlini black holes are higher-dimensional generalizations of the Schwarzschild spacetimes, comprising a static, spherically symmetric family of black hole solutions to higher-dimensional 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 Schwarzschild-Tangherlini black holes, part of ongoing joint work with Pei-Ken Hung and Mu-Tao Wang.

11/14/2018 Niky Kamran

(McGill)

Title: Lorentzian Einstein metrics with prescribed conformal infinity

Abstract: We prove a local well-posedness theorem for the $(n+1)$-dimensional Einstein equations in Lorentzian signature, with initial data whose asymptotic geometry at infinity is similar to that anti-de Sitter (AdS) space and compatible boundary data prescribed at the time-like conformal boundary of space-time. This extends the fundamental result of Friedrich on the existence of anti-de Sitter space-times in 3+1 dimensions to arbitrary space-time 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 quasi-local 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 quasi-local 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 quasi-local mass,
the Bartnik mass and the Wang-Yau mass. The talk is based on joint work
with Siyuan Lu.

 

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