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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 post-Newtonian and post-Minkowskian 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 N-body system, to obtain the equations
of motion satisfied by these bodies, and to extract the gravitational waves
generated by these motions. Black-hole 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 self-force 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 post-Newtonian 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 higher-dimensional 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 post-Newtonian
approximations, and through the numerical calculation of new self-force
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 black-hole perturbation theory
is applied to the stability of black holes, it is assumed that the underlying
system of partial differential equations admits a well-posed initial-value
problem. As another example, the convergence of the post-Newtonian 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 cross-polinate 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 |
Friedrich-Schiller 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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