General Relativity Seminar

Beginning immediately, until at least April 30, all seminars will take place virtually, through Zoom. 

During the Fall 2019 Semester, a weekly seminar will be held on General Relativity. The seminar will take place at on Fridays at 10:30am virtually. Please email the seminar organizers to obtain a link. This seminar is organized by Aghil Alaee.

To learn how to attend this seminar, please fill out this form.

The schedule will be updated below.

Spring 2020:

2/7/2020Lan-Hsuan Huang (University of Connecticut)Title: Improvability of the dominant energy scalar and Bartnik’s stationary conjecture  

Abstract: In this talk, we will introduce the concept of improvabilty of the dominant energy scalar and discuss strong consequences of non-improvability. We employ new, large families of deformations of the modified Einstein constraint operator and show that, generically, their adjoint linearizations are either injective, or else one can prove that kernel elements satisfy a “null-vector equation”. Combined with a conformal argument, we make significant progress toward Bartnik’s stationary conjecture. More specifically, we prove that a Bartnik minimizing initial data set can be developed into a spacetime that both satisfies the dominant energy condition and carries a global Killing field. We also show that this spacetime is vacuum near spatial infinity. This talk is based on the joint work with Dan Lee.

2/14/2020Yuewen Chen (CMSA)Title: Solutions of Jang’s Equation Inside Black Holes

Abstract: Jang’s equation is a degenerate elliptic differential equation which plays an important role in the positive mass theorem. In this talk, we describe a high order WENO (Weighted Essentially Non-Oscillatory) scheme for the Jang’s equation. Some special solutions will be shown, such as those possessing spherical symmetry and axial symmetry.





Alex Lupsasca (Harvard)Title: The Kerr Photon Ring

Abstract: The Event Horizon Telescope image of the supermassive black hole in the galaxy M87 is dominated by a bright, unresolved ring. General relativity predicts that embedded within this image lies a thin “photon ring,” which is itself composed of an infinite sequence of self-similar subrings. Each subring is a lensed image of the main emission, indexed by the number of photon orbits executed around the black hole. I will review recent theoretical advances in our understanding of lensing by Kerr black holes, based on arXiv:1907.04329, 1910.12873, and 1910.12881. In particular, I will describe the critical parameters γ, δ, and τ that respectively control the demagnification, rotation, and time delay of successive lensed images of a source. These observable parameters encode universal effects of general relativity, which are independent of the details of the emitting matter and also produce strong, universal signatures on long interferometric baselines. These signatures offer the possibility of precise measurements of black hole mass and spin, as well as tests of general relativity, using only a sparse interferometric array such as a future extension of the EHT to space.

2/28/2020Po-Ning Chen (University of California, Riverside)Title: A quasilocal charged Penrose inequality

Abstract: In this talk, we will discuss a quasi-local Penrose inequality with charges for time-symmetric initial data of the Einstein-Maxwell equation. Namely, we derive a lower bound for Brown-York type quasi-local mass in terms of the horizon area and the electric charge. The inequality we obtained is sharp in the sense that equality holds for surfaces in the Reissner-Nordström manifold. This talk is based on joint work with Stephen McCormick.




Nikolaos Athanasiou (University of Oxford)Title: A scale-critical trapped surface formation criterion for the Einstein-Maxwell system

Abstract: Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a recent result, in collaboration with Xinliang An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system.

3/13/2020Hsin-Yu Chen (BHI)This meeting will be taking place virtually on Zoom.
3/27/2020Sven Hirsch (Duke University)This meeting will be taking place virtually on Zoom.

Title: The spacetime positive mass theorem and path connectedness of initial data sets.

Abstract: The purpose of this talk is twofold: First we present a new proof of the spacetime positive mass theorem (joint with Demetre Kazaras and Marcus Khuri); second we discuss some new results about the topology of initial data sets (joint with Martin Lesourd).The spacetime positive mass theorem that the mass of an initial data set is non-negative with equality if and only if the initial data set arises as subset of Minkowski space. This result has first been proven by Schoen and Yau using Jang’s equation. There are further proofs by Witten using spinors and by Eichmair, Huang, Lee and Schoen using MOTS. Our proof uses Stern’s integral formula technique and also leads to a new explicit lower bound of the mass which is even valid when the dominant energy condition is not satisfied. A central conjecture in mathematical relativity is the final state conjecture which states that initial data sets will eventually approach Kerr black holes. In particular, this would imply that the space of initial data sets is path connected. Building upon the work of Marques and using deep and beautiful results of Carlotto and Li, we show that indeed the space of initial data set with compact trapped interior boundary is path connected.

4/3/2020Hyun Chul Jang (University of Connecticut)This meeting will be taking place virtually on Zoom.

Title: Mass rigidity of asymptotically hyperbolic spaces and some splitting theorems

Abstract: In this talk, we will discuss the rigidity of positive mass theorem for asymptotically hyperbolic manifolds. That is, if the mass equality holds, then the manifold is isometric to hyperbolic space. The proof used a variational approach with the scalar curvature constraint. It also involves an investigation on a type of Obata’s equations, which leads to recent splitting results with Galloway. This talk is based on the joint works with L.-H. Huang and D. Martin, and with G. J. Galloway.

4/10/2020Chao Li (Princeton)This meeting will be taking place virtually on Zoom.  

Title: Positive scalar curvature and the dihedral rigidity conjecture

Abstract: In 2013, Gromov proposed a dihedral rigidity conjecture, aiming at establishing a geometric comparison theory for metrics with positive scalar curvature. The conjecture states that if a Riemannian polyhedron has nonnegative scalar curvature in the interior, and weakly mean convex faces, then the dihedral angle between adjacent faces cannot be everywhere less than the corresponding Euclidean model. I will prove this conjecture for a large collection of polytopes. The strategy is to relate this conjecture with a geometric variational problem of capillary type, and apply the Schoen-Yau minimal slicing technique for manifolds with boundary. Our result is a localization of the positive mass theorem.

4/17/2020Brian Allen (University of Hartford)




This meeting will be taking place virtually on Zoom.

Title: Null distance and convergence of warped product spacetimes.

Abstract: The null distance was introduced by Christina Sormani and Carlos Vega as a way of turning a spacetime into a metric space. This is particularly important for geometric stability questions relating to spacetimes such as the stability of the positive mass theorem. In this talk, we will describe the null distance, present new properties of the metric space structure, and examine the convergence of sequences of warped product spacetimes equipped with the null distance. This is joint work with Annegret Burtscher.

4/24/2020Daniel Stern (University of Toronto)




This meeting will be taking place virtually on Zoom.

Title: Scalar curvature and harmonic functions

Abstract: We’ll discuss a new technique for relating scalar curvature bounds to the global structure of 3-dimensional manifolds, exploiting a relationship between the scalar curvature and the topology of level sets of harmonic functions. We will describe several geometric applications in both the compact and asymptotically flat settings, including a simple and effective new proof (joint with Bray, Kazaras, and Khuri) of the three-dimensional Riemannian positive mass theorem.

5/1/2020Demetre Kazaras (Stony Brook University)




This meeting will be taking place virtually on Zoom.

Title: Desingularizing 4-manifolds with positive scalar curvature

Abstract: We study 4-manifolds of positive scalar curvature (psc) with severe metric singularities along points and embedded circles, establishing a desingularization process. To carry this out, we show that the bordism group of closed 3-manifolds with psc metrics is trivial, using scalar-flat K{\”a}hler ALE surfaces recently discovered by Lock-Viaclovsky. This allows us to prove a non-existence result for singular psc metrics on enlargeable 4-manifolds, partially confirming a conjecture of Schoen.

5/8/2020Anna Sakovich (Uppsala University)This meeting will be taking place virtually on Zoom.  

Title: The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting

Abstract:  We will be concerned with asymptotically hyperbolic ‘hyperboloidal’ initial data for the Einstein equations. Such initial data is modeled on the upper unit hyperboloid in Minkowski spacetime and consists of a Riemannian manifold (M, g) whose geometry at infinity approaches that of hyperbolic space, and a symmetric 2-tensor K representing the second fundamental form of the embedding into spacetime, such that K -> g at infinity. There is a notion of mass in this setting and a positive mass conjecture can be proven by spinor techniques. Other important results concern the case K = g, where the conjecture states that an asymptotically hyperbolic manifold whose scalar curvature is greater than or equal to that of hyperbolic space must have positive mass unless it is a hyperbolic space. In this talk, we will discuss how the method of Jang equation reduction, originally devised by Schoen and Yau to prove the positive mass conjecture for asymptotically Euclidean initial data sets, can be adapted to the asymptotically hyperbolic setting yielding a non-spinor proof of the respective positive mass conjecture. We will primarily focus on the case dim M = 3.





Xinliang An (National University of Singapore)This meeting will be taking place virtually on Zoom.

Title: On curvature blow-up rates in gravitational collapse

Abstract: In this talk, I will present two new results on the gravitational collapse of the spherically symmetric Einstein-scalar field system. i) With Ruixiang Zhang we show that even in the most singular scenario, along the singular boundary $r=0$, the Kretschmann scalar would obey polynomial blow-up upper bounds $O(1/r^N)$. This improves previously best-known double-exponential upper bounds $O\big(\exp\exp(1/r)\big)$. Our result is sharp in the sense that there are known examples showing that no sub-polynomial upper bound could hold. ii) With Dejan Gajic, we extend the aforementioned result to a global one and calculate the precise polynomial rate-$N$. We find that, when it is close to the timelike infinity, the blow-up rates of Kretschmann scalar could be different from the Schwarzschild value. In particular, the blow-up rates are not limited to discrete finite choices and they are related to the Price’s law along the event horizon. This indicates a new blow-up phenomenon, driven by a PDE mechanism, rather than an ODE mechanism.
5/15/2020Dejan Gajic (University of Cambridge)This meeting will be taking place virtually on Zoom.  

Title: Polynomial tails and conservation laws of waves on black holes

Abstract: In 1972, Price suggested that inverse polynomial tails should be present in the late-time behaviour of scalar fields on Schwarzschild black holes. In the decades since, many features of these tails have been explored both numerically and heuristically in more general settings. The presence of polynomial tails in the context of the Einstein equations has important implications for the nature of singularities inside dynamical black holes and the late-time behaviour of gravitational waves observed at infinity. In this talk I will discuss recent work in collaboration with Y. Angelopoulos and S. Aretakis that establishes rigorously the existence of Price’s polynomial late-time tails in the context of scalar fields on black holes. I will moreover describe how late-time tails are connected to the existence of conservation laws for scalar fields in asymptotically flat spacetimes.

Grigorios Fournodavlos (Sorbonne) This meeting will be taking place virtually on Zoom.  

Title: Construction and (partial) stability of spacelike singularities

Abstract: The presence of singularities in solutions to the Einstein equations is related to profound conjectures in the field, like strong cosmic censorship. They are typically found in the interior of black holes or Big Bang models. Their nature is an often debated topic, with various rivaling scenarios arising, such as null vs spacelike or Kasner-like vs oscillatory. In the first part of the talk, we will discuss the black hole interior problem and present a recent partial stability result of the Schwarzschild singularity (joint with Spyros Alexakis). In the second part of the talk, we will move on to the cosmological setting and present a general method of constructing Kasner-like singularities without symmetries or analyticity (joint with Jonathan Luk).spacetimes.


Information about last year’s seminar can be found here.

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