May  6, 2021


Perturbation methods in General Relativity
May 19 - 22 and May 25-29, 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

Chad Galley, California Institute of Technology
Leor Barack, University of Southampton


On-line Registration open to May 10
also on-site during Focus Weeks
$100 registration fees, students and PDF $50

*Please note that a nominal registration fee is required of all participants for this Focus Program. Your contributions allow us to provide the Program with refreshments and social events for each of the Focus Weeks.
Application for Participant support
Deadline to apply April 30, 2015
Accommodation in Toronto Information for speakers Reimbursement information for funded participants Map to Fields

Focus session homepage, schedule and talk sign-up form are hosted externally at Caltech University:


Request to give a "sign-up" talk


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
  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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