Overview
Black holes are one of the most celebrated predictions of general relativity.
It is widely believed that spacetime in the vicinity of these black holes
can be described to a suitable approximation by a Kerr metric, a remarkable
family of explicit solutions of the Einstein vacuum equations discovered
in 1963. Yet even the most basic mathematical questions about the dynamics
of the Einstein equations in a neighbourhood of these solutions remain to
this day unanswered. Are the Kerr metrics stable as solutions of the Einstein
equations? Does gravitational collapse generically lead to black holes,
or can socalled "naked singularities" form instead? What happens
to observers who enter black hole regions? The latter two questions probe
the very limits of the theory and are tied to the more general issue of
singularities and the celebrated cosmic censorship conjectures of Penrose.
The last few years has seen intense activity which has brought us to the
threshold of a denitive resolution of some of these issues. After intense
work by several groups, and using important insights from the physics literature,
the decay properties of linear scalar fields on the Kerr exterior backgrounds
are now denitively mathematically understood. Concerning the problem of
gravitational collapse, a breakthrough recent theorem of Christodoulou proves
that trapped surfaces can from from initial data which are arbitrarily dispersed.
This work introduces methods for rigorously understanding the Einstein equations
in the large field regime, and already has given several applications to
other problems involving singularities. Regarding the black hole interior,
heuristic, numerical, and now rigorous mathematical theorems have shed light
on the singular boundary, denitively showing that it always has a null piecein
contrast to older expectations that singularities should generically be
everywhere spacelike.
Participants
as of June 3, 2015
* Indicates
not yet confirmed

Full Name 
University/Affiliation 

Spyros Alexakis 
University of Toronto 

Stefanos Aretakis 
Princeton University 

Piotr Bizon 
Jagiellonian University 

Pieter Blue 
University of Edinburgh 

Wilson Brenna 
University of Waterloo 

Alex Buchel 
University of Western Ontario 
* 
Vitor Cardoso 
Universidade Tecnica de Lisboa 
* 
Paul Chesler 
Harvard University 
* 
Demetrios Christodolou 
ETH Zurich 

Dominic Dold 
Cambridge University 

Semyon Dyatlov 
Massachusetts Institute of Technology 

Roberto Emparan 
Universitat de Barcelona 

Grigorios Fournodavlos 
University of Toronto 

Valeri Frolov 
University of Alberta 

Dejan Gajic 
University of Cambridge 

David Garfinkle 
Oakland University 

Gary Gibbons 
University of Cambridge 

Stephen Green 
Perimeter Institute for Theoretical Physics 

Hafner Häfner 
Universite de Grenoble 

Stefan Hollands 
Universitaet Leipzig 

Gustav Holzegel 
Imperial College London 

Jim Isenberg 
University of Oregon 

Soichiro Isoyama 
University of Guelph 

Thomas Johnson 
Imperial College London 

Jordan Keller 
Columbia University 

Gabor Kunstatter 
University of Winnipeg 

Luis Lehner 
Perimeter Institute 

Adam Lewis 
University of Toronto 

Steven Liebling 
Long Island University 

Hans Lindblad 
Johns Hopkins University 

Jonathan Luk 
University of Cambridge 

Georgios Moschidis 
Princeton University 

Oscar Reula 
Universidad Nacional de Cordoba 
* 
Igor Rodnianski 
Princeton University 

Volker Schlue 
University of Toronto 

Jacques Smulevici 
Université ParisSud 

Martin Taylor 
Cambridge University 

Robert Wald 
University of Chicago 

Claude Warnick 
Warwick University 

Helvi Witek 
University of Cambridge 
Monday,
June 8 
8:309:15

On site registration and morning coffee 
9:159:30

Welcoming remarks 
9:3010:30

Stefanos Aretakis, Princeton University
On linear and nonlinear wave equations on black
holes 
10:3011:00

Coffee break 
11:0012:00

Dietrich Häfner, Universite de
Grenoble
Scattering theory for Dirac and KleinGordon fields
on the (De Sitter) Kerr metric 
12:002:00

Lunch break 
2:003:00

Helvi Witek, University of Cambridge
The ``Blackhole bomb'' mechanism in astrophysical
environments

3:003:30

Coffee break 
3:304:30

open 
Tuesday, June 9 
9:3010:30

Semyon Dyatlov, Massachusetts
Institute of Technology
Quasinormal modes: the spectrum of Kerrde Sitter
black holes 
10:3011:00

Coffee break 
11:0012:00

Roberto Emparan,
Universitat de Barcelona
Black hole stability: largeD approach

12:002:00

Lunch break 
2:003:00

Dejan Gajic, University
of Cambridge 
3:003:30

Coffee break 
3:304:30

open 
Wednesday,
June 10 
9:3010:30

Stefan Hollands,
Universitaet Leipzig
Dynamical vs. Thermodynamical Instabilities of Black
Objects 
10:3011:00

Coffee break 
11:0012:00

Valeri Frolov, University
of Alberta
Small mass collapse in the ghostfree gravity 
12:002:00

Lunch break 
2:003:00

open 
3:003:30

Coffee break 
3:304:30

open 
Thursday,
June 11 
09:3010:30

Claude Warnick, Warwick
University
Stability problems in antide Sitter space times
(Overview) 
10:3011:00

Coffee break 
11:0012:00

Stephen Green, Perimeter
Institute for Theoretical Physics
Twotimescale analysis of AdS (in)stability: Conserved

12:002:00

Lunch break 
2:003:00

Piotr Bizon, Jagiellonian
University
New evidence for the instability of AdS 
3:003:30

Coffee break 
3:304:30

Nils Deppe, Cornell
University
TwoMode Initial Data and Massive Scalar Fields
in AdS 
5:006:00

Xinliang An,
Rutgers University
Formation of Trapped Surfaces in General Relativity

Friday,
June 12 
09:3010:30

Alex Buchel, Perimeter
Institute for Theoretical Physics
Black hole spectra in holography: consequences
for equilibration of dual gauge theories 
10:3011:00

Coffee break 
11:0012:00

Gabor Kunstatter,
University of Winnipeg
Stability of AdS in Einstein Gauss Bonnet Gravity

12:002:00

Lunch break 
2:003:00

Arick Shao, Imperial
College London
Unique Continuation in Asymptotically Antide Sitter
Spacetimes 
3:003:30

Coffee break 
3:304:30

Jacques Smulevici,
Université ParisSud
Trapping, decay and stability problems in asymptotically AdS spacetimes

Abstracts
Xinliang An, Rutgers University
Formation of Trapped Surfaces in General Relativity
In this talk, I will present two results regarding the formation of trapped
surfaces in general relativity.
The first is a simplified approach to Christodoulou’s monumental result
which showed that trapped surfaces canform dynamically by the focusing of
gravitational radiation from past null infinity. We extend the methods of
KlainermanRodnianski, who gave a simplified proof of this result in a finite
region.
The second result extends the theorem of Christodoulou by allowing for weaker
initial data but still guaranteeing that a trapped surface forms in the
causal domain. In particular, we show that a trapped surface can form dynamically
from initial data which is merely large in a scaleinvariant way. The second
result is obtained jointly with Luk.
Stefanos Aretakis, Princeton University
On linear and nonlinear wave equations on black holes
I will present some recent results on linear and nonlinear wave equations
on extremal and subextremal black hole backgrounds.
Piotr Bizon, Jagiellonian University
New evidence for the instability of AdS
Four years ago Andrzej Rostworowski and I conjectured that AdS is unstable
under arbitrarily small perturbations. In my talk (based on yet unpublished
joint work with Maciej Maliborski and Andrzej Rostworowski) I will present
a new piece of evidence supporting our conjecture.
Alex Buchel, Perimeter Institute for Theoretical
Physics
Black hole spectra in holography: consequences for equilibration of dual
gauge theories
For a closed system to equilibrate from a given initial conditionthere must
exist an equilibrium state with the energy equal to theinitial one. Equilibrium
states of a strongly coupled gauge theorywith a gravitational holographic
dual are represented by black holes.We study the spectrum of black holes
in PilchWarner geometry. Theseblack holes are holographically dual to equilibrium
states of stronglycoupled SU(N) N=2^* gauge theory plasma on S^3 in theplanar
limit. We find that there is no energy gap in the black holespectrum. Thus,
there is a priory no obstruction for equilibration ofarbitrary lowenergy
states in the theory via a small black holegravitational collapse. The latter
is contrasted withphenomenological examples of holography with dual fourdimensionalCFTs
having nonequal central charges in the stressenergy tensortrace anomaly.
Nils Deppe, Cornell University
TwoMode Initial Data and Massive Scalar Fields in AdS
It has been argued that antide Sitter spacetime in general relativity
is unstable against the formation of black holes for arbitrarily small perturbations,
at least for a large class of initial data. Stable evolution has been observed
for initial data of the form of a single Gaussian within a range of widths,
boson stars, specially constructed timeperiodic solutions, and certain
superpositions of multiple Gaussian wavepackets. We perform a detailed study
of the single Gaussian, multiple Gaussian and two eigenmode initial data
using the energy per mode to quantify the dynamics. We find interesting
and unexpected chaotic behaviour, as well as the previously predicted inverse
cascade of energy to lower modes. Additionally, we study massive scalar
field perturbations over a range of masses and different forms of initial
data, finding qualitatively similar results to the massless case for smaller
masses, but different behaviour for extremely massive fields.
Semyon Dyatlov, Massachusetts Institute of
Technology
Quasinormal modes: the spectrum of Kerrde Sitter black holes
Consider linear waves on the Kerrde Sitter spacetime, which models a rotating
black hole with a positive cosmological constant. In contrast with the Kerr
solution, solutions to the wave equation decay exponentially up to a finite
dimensional subspace. This makes it possible to expand waves asymptotically
in terms of quasinormal modes, which are the complex characteristic frequencies
associated to the spacetime. I present several recent results, giving a
rigorous definition of quasinormal modes and describing their asymptotic
behavior in the high frequency limit. The high frequency picture relies
on the normally hyperbolic structure of the set of trapped light rays.
Roberto Emparan, Universitat de Barcelona
Black hole stability: largeD approach
After introducing the main elements of the large D approach to black hole
physics, I will focus on its use in the analysis of mode stability of black
holes. This is greatly simplified, by isolating the modes that are potentially
stable, and by drastically simplifying their equations.
Valeri Frolov, University of Alberta
Small mass collapse in the ghostfree gravity
We discuss a problem of a black hole formation in the ghostfree gravity.
We demonstrate how a nonlocal modification of gravity equations regularizes
static and dynamical solutions. We focus on the problem of a collapse of
small masses in the ghostfree gravity, and demonstrate that there exists
a mass gap for miniblackhole formation in this model.
Stephen Green, Perimeter Institute for Theoretical
Physics
Twotimescale analysis of AdS (in)stability: Conserved
We consider the dynamics of a spherically symmetric massless scalarfield
coupled to general relativity in anti–de Sitter spacetime in thesmallamplitude
limit. We first develop the "two time framework" (TTF)approximation
to study the leading selfgravitating effects of thescalar field. Within
this context, we uncover the presence of 3conserved quantities: the energy
E, the particle number N, and theHamiltonian H. Simultaneous conservation
of E and N implies thatweakly turbulent processes undergo dual cascades
(direct cascade of Eand inverse cascade of N or vice versa), and it rules
out energyequipartition for generic initial data. Furthermore, TTF admits
alarge class of quasiperiodic (QP) solutions that extremize H. Weperform
a linear stability analysis of QP solutions within TTF, and weshow that
there exist several families of stable solutions. We arguethat certain spacetime
solutions that avoid collapse (for long times)are perturbations about QP
solutions, and we use the stabilityanalysis to calculate approximate recurrence
times that have beenobserved in numerical simulations. We also discuss how
collapsingsolutions can be understood within TTF.
Dietrich Häfner, Universite de Grenoble
Scattering theory for Dirac and KleinGordon fields on the (De Sitter)
Kerr metric
I will discuss scattering theory for Dirac and KleinGordon fields on a
(perturbed) Kerr resp. DeSitter Kerr metric. Asymptotic completeness results
are obtained for both the Dirac field and the KleinGordon field, where
for the KleinGordon field the angular momentum of the field has to be fixed.
For the Dirac field I will explain the equivalence between the classical
formulation in terms of direct and inverse wave operators and the interpretation
as an existence and uniqueness result for the Goursat problem at null infinity.
For the KleinGordon field I will explain how superradiance can be understood
in terms of spectral theory using an appropriate functional calculus. If
there is enough time I will also discuss the link between the Hawking effect
and scattering theory on a spacetime describing a collapsing star. The
talk is based on joint work with JeanPhilippe Nicolas (Dirac fields) and
Vladimir Georgescu, Christian Gérard (KleinGordon fields).
Stefan Hollands, Universitaet Leipzig
Dynamical vs. Thermodynamical Instabilities of Black Objects
Black holes are well known to have properties that are strikingly similar
to the ordinary laws of phenomenological thermodynamics. These properties
are therefore often referred to as the "laws of black hole mechanics,"
and play a key role in many attempts to quantize gravity. However, as has
been appreciated more recently, appropriate extensions of these laws can
also be used to understand the *dynamical properties* of *classical* black
holes as well as their higher dimensional counterparts. Such ideas suggest
that simple, and standard, criteria for thermodynamical instability as formulated
in ordinary phenomenological thermodynamics ('negative heat capacity') are
informative also for the  technically very challenging  analysis of
the stability properties of black holes or even stars. In this talk, I will
review these kinds of ideas, their motivation, and applications to several
interesting examples including a) (near) extremal, rotating BHs in higher
dimensions, b) super radianttype instabilities for AdS BHs. In particular,
I will argue that the famous laws of black hole mechanics should be supplemented
by a further analogy relating thermodynamical and dynamical instability.
Gabor Kunstatter, University of Winnipeg
Stability of AdS in Einstein Gauss Bonnet Gravity
Authors: Nils Deppe, Allison Kolly, Andrew Frey, and Gabor Kunstatter
Recently it has been argued that in Einstein gravity Antide Sitter spacetime
is unstable againstthe formation of black holes for a large class of arbitrarily
small perturbations. We have recently examined the effects of a change in
the small scale gravitational dynamics on stability by adding a Gauss Bonnet
term to the action. In five dimensions, spherically symmetric EinsteinGaussBonnet
(EGB) gravity has two key features: Choptuik scaling exhibits a radius gap,
and the mass function goes to a finite value as the horizon radius vanishes.
These suggest that black holes will not form dynamically if the total mass/energy
content of the spacetime is too small, thereby restoring the stability of
AdS spacetime for large families of generic initial data. After a brief
review, I will present numerical evidence to support this claim. Our numerical
simulations have uncovered a rich structure in horizon radii and formation
times as a function of perturbation amplitude. Although our calculations
were specific to 5D EGB, I will argue that the qualitative behaviour we
observed is likely to exist in a large class of theories in which the microscopic
dynamics is governed by a new length scale.
Arick Shao, Imperial College London
Unique Continuation in Asymptotically Antide Sitter Spacetimes
In this talk, we consider the problem of unique continuation from infinity
for Antide Sitter (AdS) and asymptotically AdS spacetimes. We show, roughly,
that given a solution $\phi$ of a linear (massive or massless) wave equation
on AdS spacetime, if $\phi$ and its first derivative vanish to high enough
order (depending on the mass) on a sufficiently large but finite portion
of infinity, then $\phi$ must also necessarily vanish in a small neighborhood
of infinity. In particular, this establishes a correspondence between data
for $\phi$ at infinity and the value of $\phi$ in the interior.
When available, we also connect our results to the wellposedness theory:
we show that trivial Dirichet and Neumann data at (a large enough portion
of) infinity along with sufficient regularity implies vanishing in the interior.
Furthermore, all these results generalize to a large class of asymptotically
AdS spacetimes, as well as to tensorvalued waves. These techniques are
also viable for studying nonlinear wave equations; one application is to
study corresponding uniqueness properties for the Einsteinvacuum equations
with negative cosmological constant.
This is joint work with Gustav Holzegel.
Claude Warnick, Warwick University
Stability problems in antide Sitter space times (Overview)
Over recent years there has been considerable progress in understanding
solutions of Einstein’s equations with negative cosmological constant.
The presence of a timelike conformal boundary for these spacetimes introduces
many novel features to the classical evolution problem. In particular, questions
of dynamical stability are intimately tied to the structure of infinity.
In this talk I will give an overview of recent work on the stability problem
for AdS spacetimes, including numerical and analytic results. I will in
particular discuss the connection of the stability problem with the structure
of null infinity.
Helvi Witek, University of Cambridge
The ``Blackhole bomb'' mechanism in astrophysical environments
Many fundamental questions concerning the (nonlinear) stability of black
holes (BHs) even in fourdimensional spacetimes are still unanswered. In
particular, rotating black holes may suffer from the superradiant or ``BHbomb''
type instability in the presence of massive fields.These fields appear naturally
in modifications of General Relativity, where interactions with the environment
bestow them with an effective mass, or in extensions of the standard model
predicting additional ultralight bosonic field, such as axionlike particles
or dark matter candidates.
In this talk, I will discuss phenomena resulting from the interaction between
BHs and massive fields (both in the linear and nonlinear regime),such as
the development of longlived bosonic condensates whose presence may lead
to gaps in the BH Reggeplane or the induction of characteristic gravitational
wave signals, that may transform astrophysical BHs into ``laboratories''
to hunt for beyond standard model physics.
Back to top