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Overview
The use of perturbation techniques in General Relativity dates back to
the very beginnings, when the weak nature of gravity and the slow motion
of planets in the solar system were exploited to build approximation methods.
Since then these methods have been refined, and new methods have been invented
to solve new problems.
For instance, the postNewtonian and postMinkowskian formalisms aim to
find approximate solutions to the Einstein field equations when the gravitational
field is weak and the motion of bodies is slow. These formalisms have been
exploited to calculate the metric of an Nbody system, to obtain the equations
of motion satisfied by these bodies, and to extract the gravitational waves
generated by these motions. Blackhole perturbation theory describes an
isolated black hole perturbed slightly by nearby objects, and it has produced
a host of interesting phenomena such as the quasinormal ringdown of black
holes, the gravitational waves emitted by a body in very rapid motion in
the black hole's very strong field, and the gravitational selfforce acting
on this body. Recently, the powerful body of techniques known as effective
field theory, first developed in the context of quantum field theory, have
been imported to General Relativity and have profitably informed the traditional
perturbative approaches. While these techniques are all approximations that
rely on the existence of a smallness parameter (such as the ratio of velocities
to the speed of light in the case of postNewtonian theory, or the mass
ratio in the case of a black hole perturbed by a small body), a different
kind of approximation is delivered when the Einstein field equations are
discretized and solved on supercomputers.
The recent breakthroughs of numerical relativity have allowed us to understand
the rich dynamics of the gravitational field during black hole collisions,
the instability of higherdimensional black strings, and is now shedding
light on the interaction between neutron stars, their accretion disks, and
their magnetic fields. Numerical relativity is also increasingly informing
the perturbative methods, for instance through comparisons with postNewtonian
approximations, and through the numerical calculation of new selfforce
results.
These methods are all being applied to improve our understanding of Einstein's
equations and their practical applications, but they rely strongly on either
known or believed fundamental properties of the underlying mathematical
structure of the theory. For instance, when blackhole perturbation theory
is applied to the stability of black holes, it is assumed that the underlying
system of partial differential equations admits a wellposed initialvalue
problem. As another example, the convergence of the postNewtonian sequence
of approximations is still an open problem awaiting mathematical attention.
It is clear that a close dialogue between the physical and mathematical
communities is important, as this will help further not only the individual
research agendas but also crosspolinate ideas and problems through dialogue,
discussions, and collaborations.
Participants
as of May 13, 2015
* Indicates
not yet confirmed

Full Name

University/Affiliation


Leor Barack 
University of Southampton 

Luc Blanchet 
Institut d'Astrophysique de Paris 

Sam Dolan 
University of Sheffield 

Grigorios Fournodavlos 
University of Toronto 

Chad Galley 
California Institute of Technology 

Walter Goldberger 
Yale University 

Stephen Green 
Perimeter Institute for Theoretical Physics 

Abraham Harte 
Albert Einstein Institute 

David Hiditch 
FriedrichSchiller University of Jena 

Tanja Hinderer 
Max Planck Institute for Gravitational Physics
(Albert Einstein Institute) 

Soichiro Isoyama 
University of Guelph 

Philippe Landry 
University of Guelph 

Alexandre Le Tiec 
Observatoire de Paris 

Raissa Mendes 
University of Guelph 

Carlos Palenzuela 
Universitat de les Illes Balears 

Paolo Pani 
Sapienza University of Rome 

Adam Pound 
University of Southampton 
* 
Ira Rothstein 
Carnegie Mellon University 

Volker Schlue 
University of Toronto 

Peter Taylor 
Cornell University 

Aaron Zimmerman 
Canadian Institute for Theoretical Astrophysics 
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