5. May 2022
Video
(City University of New York, USA)
Title: Towards a Spacetime Intrinsic Flat Convergence
Abstract: In order to define a spacetime intrinsic flat convergence,
Carlos Vega and I defined the null distance to convert spacetimes
endowed with regular cosmological times into metric spaces. Currently Anna Sakovich and I have been exploring the properties of
these metric spaces. We can prove that one can recover the causal
structure from the null distance and the cosmological time. We can
prove that a distance-preserving time-preserving bijection between the spacetimes endowed with a null distance is in fact a Lorentzian isometry under suitable conditions. Next we will prove there are
biLipschitz charts so that we may view the spacetimes endowed with the null distance as integral current spaces. This allows us to rigorously define the spacetime intrinsic flat convergence for
spacetimes that arise as the future maximal developments of initial
data sets. For more information about intrinsic flat convergence see https://sites.google.com/site/intrinsicflatconvergence/
7. April 2022
Video
ROBERT WALD
(The University of Chicago, USA)
Title: The Memory Effect and Infrared Divergences
Abstract: The “memory effect” is the permanent relative displacement of test particles after the passage of gravitational radiation. It is associated with both the propagation of massive bodies out to timelike infinity (“ordinary memory”) or the propagation of radiation out to null infinity (“null memory”). The memory effect can be characterized by the failure of the shear tensor at order 1/r to return to zero at late times, even though it is “pure gauge.” Closely analogous effects occur in electromagnetism, where the vector potential at order 1/r fails to return to zero even though it is “pure gauge.” In both cases, the Fourier transform of the radiative field has divergent behavior at low frequencies. This gives rise to infrared divergences (i.e., infinite numbers of “soft” gravitons/photons) in the quantum field theory description if one attempts to describe these states as vectors in the usual Fock Hilbert space representation. To obtain a mathematically sensible quantum scattering theory, one must allow states with nonvanishing memory in the “in” and “out” Hilbert spaces. An elegant solution to this problem in massive quantum electrodynamics was given by Kulish and Fadeev, who constructed a Hilbert space of incoming/outgoing charged particle states that are “dressed” with radiative fields of corresponding memory, so as to yield vanishing large gauge charges at spatial infinity. However, we show that this type of construction fails in quantum gravity. The primary underlying reason is that the “dressing” contributes to null memory, thereby invalidating the construction of eigenstates of large gauge charges. In quantum gravity, there does not appear to be any choice of (separable) Hilbert space of incoming/outgoing states that can accommodate all scattering states. Thus, we argue that scattering should be described at the level of algebraic incoming/outgoing states rather than attempting to artificially restrict states to a particular Hilbert space.
3. March 2022
Video
ZOE WYATT
Title: Global Stability of Spacetimes with Supersymmetric Compactifications
Abstract: Spacetimes with compact directions which have special holonomy, such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss a recent work with Lars Andersson, Pieter Blue and Shing-Tung Yau, where we show the global, nonlinear stability a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This stability result is related to a conjecture of Penrose concerning the validity of string theory. Our proof uses the intersection of methods for quasilinear wave and Klein-Gordon equations, and so towards the end of the talk I will also comment more generally on coupled wave–Klein-Gordon equations.
3. February 2022
Video
ERIC LING
Title: On the discrete Dirac spectrum of a point electron in the zero-gravity Kerr-Newman spacetime
Abstract: In relativistic quantum mechanics, the discrete spectrum of the Dirac hamiltonian with a Coulomb potential famously agrees with Sommerfeld’s fine structure formula for the hydrogen atom. In the Coulomb approximation, the proton is assumed to only have a positive electric charge. However, the physical proton also appears to have a magnetic moment which yields a hyperfine structure of the hydrogen atom that’s normally computed perturbatively. Aiming towards a non-perturbative approach, Pekeris in 1987 proposed taking the Kerr-Newman spacetime with its ring singularity as a source for the proton’s electric charge and magnetic moment. Given the proton’s mass and electric charge, the resulting Kerr-Newman spacetime lies well within the naked singularity sector which possess closed timelike loops. In 2014 Tahvildar-Zadeh showed that the zero-gravity limit of the Kerr-Newman spacetime (zGKN) produces a flat but topologically nontrivial spacetime that’s no longer plagued by closed timelike loops. In 2015 Tahvildar-Zadeh and Kiessling studied the hydrogen problem with Dirac’s equation on the zGKN spacetime and found that the hamiltonian is essentially self-adjoint and contains a nonempty discrete spectrum. In this talk, we show how their ideas can be extended to classify the discrete spectrum completely and relate it back to the known hydrogenic Dirac spectrum but yielding hyperfine-like and Lamb shift-like effects.
2. December 2021
Video
STEFAN CZIMEK
(ICERM, Brown University, USA)
Title: The characteristic gluing problem of general relativity
Abstract: In this talk we introduce and solve the characteristic gluing problem for the Einstein vacuum equations. We prove that obstructions to characteristic gluing come from an infinite-dimensional space of conservation laws along null hypersurfaces for the linearized equations at Minkowski. We show that this obstruction space splits into an infinite-dimensional space of gauge-dependent charges and a 10-dimensional space of gauge-invariant charges. We identify the 10 gauge-invariant charges to be related to the energy, linear momentum, angular momentum and center-of-mass of the spacetime. Based on this identification, we explain how to characteristically glue a given spacetime to a suitably chosen Kerr black hole spacetime. As corollary we get an alternative proof of the Corvino-Schoen spacelike gluing to Kerr. Moreover, we apply our characteristic gluing method to localise characteristic initial data along null hypersurfaces. In particular, this yields a new proof of the Carlotto-Schoen spacelike localization where our method yields no loss of decay, thus resolving an open problem in this direction. We also outline further applications. This is joint work with S. Aretakis (Toronto) and I. Rodnianski (Princeton).
4. November 2021
Video
MELANIE GRAF
(University of Tübingen, Germany)
Title: Singularity theorems in low regularity
Abstract: The singularity theorems of R. Penrose and S. Hawking from the 1960s show that a spacetime satisfying certain physically reasonable curvature and causality conditions cannot be causal geodesically complete. Despite their great success these classical theorems still have some drawbacks, one of them being that they require smoothness of the metric while in many physical models the metric is less regular. In my talk I will present work on singularity theorems based on distributional energy conditions for metrics that are merely continuously differentiable – a regularity where one still has existence but not uniqueness for solutions of the geodesic equation. We will see that an approximation-based approach to the low-regularity issue is closely linked to establishing singularity theorems under weakened energy conditions and while the improvements necessary are still entirely straightforward in the present case, attempting to lower the regularity further would require some new methods.
7. October 2021
Video
MIHALIS DAFERMOS
(Princeton University, USA) and (University of Cambridge, UK)
Title: The black hole stability problem in general relativity
Abstract: I will review the current status of the black hole stability problem in general relativity and discuss joint work Holzegel, Rodnianski and Taylor.
1. July 2021
Video
GEORGIOS MOSCHIDIS
3. June 2021
Video
PIOTR CHRUŚCIEL
(University of Vienna, Austria)
hyperbolic manifolds, and sketch the proof of positivity of the energy for manifolds with spherical conformal infinity.
Talk based on joint work with Erwann Delay in arXiv: 1901.05263 [math.DG]
6. May 2021
Video
LAN-HSUAN HUANG
(University of Connecticut, USA)
1. April 2021
Video
MARTÍN REIRIS
(University of the Republic, Uruguay)
4. March 2021
Video
IGOR RODNIANSKI
4. February 2021
Video
HARVEY REALL
3. December 2020
Video
LYDIA BIERI
(University of Michigan, Ann Arbor, USA)
5. November 2020
Video
GREG GALLOWAY
1. October 2020
Video
