
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
Singularities
in General Relativity
June 1518, 2015
Organizing
Committee 
Focus
Week Organizers 
Spyros
Alexakis, University of Toronto
Mihalis Dafermos, Princeton University
Luis Lehner, Perimeter Institute for Theoretical
Physics and University of Guelph
Harald Pfeiffer, Canadian Institute for Theoretical
Astrophysics (CITA)
Eric Poisson, University of Guelph

Jim
Isenberg, University of Oregon
Jonathan Luk, University of Cambridge








Overview
Details to come.
Participants
as of June 9, 2015
* Indicates
not yet confirmed

Full Name

University/Affiliation


Spyros Alexakis 
University of Toronto 

Ellery Ames 
Chalmers University 

Xinliang An 
Rutgers University 

Florian Beyer 
University of Otago 

Wilson Brenna 
University of Waterloo 
* 
Vitor Cardoso 
Universidade Tecnica de Lisboa 

João Costa 
University Institute of Lisbon 

Stefan Czimek 
Laboratoire JacquesLouis Lions, Universite
Paris 6 

Mihalis Dafermos 
Princeton University 

Dominic Dold 
Cambridge University 

Grigorios Fournodavlos 
University of Toronto 

Dejan Gajic 
University of Cambridge 

David Garfinkle 
Oakland University 
* 
Gary Gibbons 
University of Cambridge 

Cécile Huneau 
Ecole Normale Superieure 

Jim Isenberg 
University of Oregon 

Orchidea Maria Lecian 
Sapienza University of Rome 

Luis Lehner 
Perimeter Institute 

Adam Lewis 
University of Toronto 

Jonathan Luk 
University of Cambridge 
* 
Brian Markle 


SungJin Oh 
University of California, Berkeley 
* 
Amos Ori 
Technion 
* 
Harvey Reall 
University of Cambridge 

Jan Sbierski 
University of Cambridge 

Volker Schlue 
University of Toronto 

Arick Shao 
Imperial College London 

Yakov ShlapentokhRothman 
Massachusetts Institute of Technology 

Matteo Smerlak 
Perimeter Institute 
* 
Jacques Smulevici 
Université ParisSud 
* 
Jared Speck 
Massachusetts Institute of Technology 
* 
Oh Sungjin 
University of California, Berkeley 

Norihiro Tanahashi 
University of Cambridge 

Martin Taylor 
Cambridge University 

Aaron Zimmerman 
Canadian Institute for Theoretical Astrophysics 
Monday,
June 15 
2:002;45

Mihalis Dafermos, Princeton University

3:003:45

Jan Sbierski, Magdalene College, Cambridge.
The C^0 inextendibility of the Schwarzschild
spacetime

4:004:30

Coffee break 
4:305:15

Grigorios Fournodavlos, University
of Toronto
On the backward stability of the Schwarzschild
black hole singularity 
Tuesday, June 16 
10:0010:45

João Costa,
University Institute of Lisbon
On strong cosmic censorship with a cosmological
constant 
11:0011:45

Luis Lehner, Perimeter
Institute
Black hole instabilities in higher dimensions and naked singularities

12:002:00

Lunch 
2:002:45

Jonathan Luk, University
of Cambridge 
3:003:45

SungJin Oh, University
of California, Berkeley
Linear instability of the ReissnerNordström Cauchy
horizon under scalar perturbations 
4:004:30

Coffee break 
4:305:00

Discussion of Weak Null
Singularities and Strong Cosmic Censorship 
Wednesday,
June 17 
10:0010:45

Yakov ShlapentokhRothman,
Massachusetts Institute of Technology
Stability and Instability of Scalar Fields on Kerr
Spacetimes 
11:0011:45

Huan Yang, Perimeter
Institute
Holographic Insights into Black Hole Spacetimes 
12:002:00

Lunch break 
2:002:45

Norihiro Tanahashi,
University of Cambridge
Causality, Hyperbolicity and Shock Formation
in Lovelock Theories 
3:003:45

Jacques Smulevici, Université
ParisSud
On the future asymptotics of polarized T2 symmetric spacetime 
Thursday,
June 18 
10:0010:45

Jim Isenberg, University
of Oregon 
11:0011:45

Ellery Ames, Chalmers
University
The Asymptotic Value Problem for the Einstein Field
Equations and AVTD Solutions 
12:002:00

Lunch break 
2:002:45

David Garfinkle,
Oakland University 
3:003:30

Discussion of AVTD, Mixmaster,
and Strong Cosmic Censorship 
Ellery Ames, Chalmers University
The Asymptotic Value Problem for the Einstein Field Equations and AVTD
Solutions
The notion of an asymptotic value problem can be introduced in cases where
one is interested in solutions to PDE with prescribed asymptotics. The problem
of finding AVTD solutions is naturally formulated as an asymptotic value
problem for the Einstein field equations. In this case the prescribed asymptotics
are obtained from a certain set of equations called the VTD system, which
are in turn derived from the Einstein equations. In this talk I will present
the asymptotic value problem for the vacuum Einstein field equations in
wave gauges. The reason for using wave gauges is to obtain a symmetric hyperbolic
formulation, a structural condition which is key in obtaining nonanalytic
solutions. The wave gauge formulation also allows one to consider different
coordinate systems. As an example I will discuss results for AVTD solutions
in spacetimes with Gowdy symmetry. This work provides tools with which to
investigate the coordinatedependence of the VTD property, as well as establishing
smooth AVTD solutions with U(1)symmetry.
João Costa, University Institute of Lisbon
On strong cosmic censorship with a cosmological constant
Motivated by the Strong Cosmic Censorship Conjecture (SCCC) we consider
the problem of global uniqueness for the EinsteinMaxwellscalar field system
with a cosmological constant, for spherically symmetry characteristic initial
data. First we consider the situation where the outgoing data is stationary
(i.e., prescribed by a subextremal Reissner Nordstroem black hole event
horizon) and the remaining data is otherwise free. In that case, one can
find an open set of free data for which it is possible to construct regular
extensions of the maximal (globally hyperbolic) development. This provides
indirect evidence for the failure of the SCCC in the case of a positive
cosmological constant.
To go from indirect evidence to results applying unequivocally to the conjecture
at hand we present some preliminary results concerning the case where the
outgoing data, instead of stationary, satisfies Price's law.
Grigorios Fournodavlos, University of
Toronto
On the backward stability of the Schwarzschild black hole singularity
We study the backwardsintime stability of the Schwarzschild singularity
from a dynamical PDE point of view. More precisely, considering a spacelike
hypersurface $\Sigma_0$ in the interior of the black hole region, tangent
to the singular hypersurface $\{r=0\}$ at a single sphere, we study the
problem of perturbing the Schwarzschild data on $\Sigma_0$ and solving the
Einstein vacuum equations backwards in time. We obtain a local wellposedness
result for small perturbations lying in certain weighted Sobolev spaces,
without any symmetry assumptions. The perturbed spacetimes all have a singularity
at a ``collapsed'' sphere on $\Sigma_0$, where the leading asymptotics of
all geometric components match those of their Schwarzschild counterparts
to a suitably high order. This result thus yields a class of nonsymmetric
vacuum spacetimes, evolving forwardsintime from smooth initial data, which
form a Schwarzschild type singularity at a collapsed sphere. We rely on
a precise asymptotic analysis of the Schwarzschild geometry near the singularity
which appears to be just borderline for our method to be applicable.
SungJin Oh, University of California, Berkeley
Linear instability of the ReissnerNordström Cauchy horizon under
scalar perturbations
Consider the linear scalar wave equation on a fixed subextremal ReissnerNordström
spacetime with nonvanishing charge. In this talk, I will present a proof
that generic smooth and compactly supported initial data on a Cauchy hypersurface
give rise to solutions with infinite nondegenerate energy near the Cauchy
horizon in the interior of the black hole. This is a joint work with J.
Luk.
This linear instability of the Cauchy horizon is related to the celebrated
blue shift effect in the interior of the black hole. The problem is motivated
by the strong cosmic censorship conjecture, and it is expected that for
the full nonlinear EinsteinMaxwell system this instability leads to a singular
Cauchy horizon for generic small perturbations of ReissnerNordström
spacetime.
Jan Sbierski, Magdalene College, Cambridge.
The C^0 inextendibility of the Schwarzschild spacetime
The maximal analytic Schwarzschild spacetime is manifestly inextendible
as a Lorentzian manifold with a C^2 regular metric. In this talk I will
describe how one proves the stronger statement that the maximal analytic
Schwarzschild spacetime is inextendible as a Lorentzian manifold with a
continuous metric. The investigation of lowregularity inextendibility criteria
is motivated by the strong cosmic censorship conjecture.
Yakov ShlapentokhRothman, Massachusetts Institute
of Technology
Stability and Instability of Scalar Fields on Kerr Spacetimes
I will discuss some stability and instability results for wave and KleinGordon
equations on subextremal Kerr exterior backgrounds. More specifcally, for
the wave equation we will see that general finite energy solutions have
a uniformly bounded energy and satisfy an integrated local energy decay
estimate. In contrast, for the KleinGordon equation we will see that there
exist finite energy solutions which grow exponentially. We will also discuss
the implications of these results for black hole stability. Some of this
work is joint with Mihalis Dafermos and Igor Rodnianski.
Norohiro Tanahashi, University of Cambridge
Causality, Hyperbolicity and Shock Formation in Lovelock Theories
We study gravitational wave propagation in Lovelock theories, which are
extensions of Einstein's theory by highercurvature corrections, to examine
if these theories have good properties such as causality and hyperbolicity.
We study the propagation on various background spacetime, and find that
initial value problem may cease to be wellposed in some case. We also show
that the sound speed of gravitational wave depends on the background and
it may cause shock formation in these theories. We discuss implications
of these phenomena.
Huan Yang, Perimeter Institute
Holographic Insights into Black Hole Spacetimes
Motivated by the gravity/fluid correspondence, I will first discuss a new
type of nonlinear instability of rapidlyspinning black holes, which display
a inversecascading turbulentlike phenomenon. After that I will generalize
the analysis and introduce a new method to characterizing nonlinear gravitational
interaction. Namely the nonlinear perturbative form of Einstein equation
is mapped to the equation of motion of a collection of nonlinearlycoupled
harmonic oscillators. These oscillators correspond to the quasinormal or
normal modes of the background spacetime. In spacetimes with gravity/fluid
correspondence, such as AdS black branes, this formalism gives equivalent
equations of motion as the NavierStokes equation of the boundary fluid.
It is also expected to remain valid in more general spacetimes.
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