Mathematical Perspectives of Gravitation beyond the Vacuum Regime

Covid19: Despite the current health crisis, the program is still scheduled to take place as planned . The ESI team will send to the participants the hygiene measures and regulations at the ESI that we are expected to follow to ensure everyone's safety. The participants will be informed as early as possible in case of changes in the organisation of the program. Furthermore, to ensure sufficient distance between the participants, the attendance is now limited to 50 participants. 

Purpose of the thematic program:

The main aim of the program is to drive progress by connecting researchers working on different matter models and by advertising open problems that can serve as an entry point for researchers from other areas. In particular, we want to bring together people who work on {different types of }relativistic matter with {each other and with }those who work on non-relativistic matter. We believe large benefits are to be gained from increased interactions that would hopefully lead to exchanges of ideas and techniques that could be used to spur progress on outstanding problems in both areas. 

Key dates of the program:

Spring School: February 15-19, 2021; The course summaries can be found here.
Workshop: February 22-26, 2021; The preliminary list of speakers can be found here.

Please note that attendance is limited at all times to 50 participants. Hence, the attendance to the spring school and the workshop are limited to 50 persons.

The program is supported by the Faculty of Physics of the University of Vienna and Chalmers University of Technology.


Preliminary list of speakers for the workshop (February 22-26, 2021)


  • L. Andersson (AEI) 
  • M. Dafermos (Cambridge) 
  • M. Hadžić (University College London) t.b.c.
  • P. Hintz (MIT)
  • M. Kunze (Unviersity of Cologne) 
  • J. Jang (University of Southern California) 
  • P. LeFloch (Sorbonne Université)
  • H. Lindblad (John Hopkins University) 
  • J. Luk (Stanford) 
  • G. Rein (Universiy of Bayreuth) 
  • H. Ringström (KTH) t.b.c.
  • J. Smulevici (Sorbonne Université) 
  • J. Speck (Vanderbuilt) 
  • R. Strain (University of Pennsylvania) t.b.c.
  • J. Szeftel (Sorbonne Université)
  • M. Taylor (Imperial College London) 
  • A. Vasy (Stanford University)
  • Q. Wang (Oxford) 
  • S. Wu (University of Michigan)

Lectures of the spring school (Februay 15-19, 2021) 


  1. Robert Beig (Vienna), Elasticity as a relativistic matter model
  2. Markus Kunze (Cologne), The Relativistic Vlasov-Maxwell System
  3. Gerhard Rein (Bayreuth), Self-gravitating matter distributions and the Vlasov equation
  4. Jared Speck (Vanderbilt), Recent advances in the mathematical theory of relativistic and non-relativistic compressible Euler flow

Course summaries


  • Elasticity as a relativistic matter model
    Robert Beig (Uni. Vienna)
    The geometrical field theory of elasticity is a branch of continuum mechanics which describes the dynamics of solid materials. Perfect fluids can be viewed as a limiting case of elastic materials. A specific perfect fluid is defined in the simplest case by a function of one variable, the equation of state, whereas an elastic material needs a function of at least two variables. Despite this complication it is conceivable that already in the absence of gravity elasticity is better behaved under time evolution than perfect fluids since elastic materials might not generically develop shocks as fluids are believed to do. We describe the Einstein elastic system and what little is known about it.

  • On the Antonov stability estimate in galactic dynamics
    Markus Kunze (Cologne)
    In this series of lectures I am going to review various aspects of the Antonov stability estimate, a basic tool for proving nonlinear stability in galactic dynamics. In particular, for the Vlasov-Poisson system we are going to characterize the cases where the best constant in this estimate is attained, and we are going to discuss what this could mean for the overall dynamics.

  • Self-gravitating matter distributions and the Vlasov equation
    Gerhard Rein (Bayreuth)
    In astrophysics systems like globular clusters or galaxies are often modeled as a self-gravitating collisionless gas, i.e., as an ensemble of particles (stars), described by a density function on phase space, which interact only by the gravitational field which the particles create collectively. In the Newtonian set-up this results in the Vlasov-Poisson system, in the general relativistic set-up this results in the Einstein-Vlasov system.
    These systems have some remarkable properties. Both systems have a plethora of steady state solutions. For the Vlasov-Poisson system there exists a well-developed existence theory for the corresponding initial value problem, in particular, sufficiently regular data launch singularity-free, global solutions. Hence any break down of solutions of the Einstein-Vlasov system must be due to a genuinely relativistic effect and not just due to the matter model. Finally, given a plethora of steady states and some understanding of the time dependent case one can ask about the dynamical stability or instability of these steady states.
    In my lectures I will discuss some (and probably not all) of these issues.

  • Recent advances in the mathematical theory of relativistic and non-relativistic compressible Euler flow
    Jared Speck (Vanderbilt)
    The last 15 years have witnessed dramatic advances in the rigorous mathematical theory of solutions to the relativistic Euler equations and their non-relativistic analog, the compressible Euler equations. Examples of progress include i) Christodoulou’s groundbreaking 2007 monograph on shock formation for relativistic Euler solutions in irrotational and isentropic regions; ii) my work with J. Luk that extends Christodoulou’s result to the compressible Euler equations for an open set of initial data with vorticity; iii) Christodoulou’s recent resolution of the restricted shock develop- ment problem (which is essentially a local well-posedness result for irrotational and isentropic weak solutions with a shock singularity); and iv) some recent results on the existence of solutions with rough sound waves. The proofs of these results fundamentally rely on geometric formulations of the equations that exhibit remarkable structural features. The presence of these structures allows one to import insights and techniques from Lorentzian geometry, mathematical general relativity, and the theory of geometric wave equations into the study of compressible fluid mechanics, in total providing the scaffolding for the analysis in the proofs. In this course, I will survey these results and the ideas behind their proofs, and provide some indications about the trajectory of the field.


Coming soon.

This event has no subevents associated to it.
  • Håkan Andréasson (CUT, Göteborg) — Organizer
  • Robert Beig (U Vienna)
  • Pieter Blue (U Edinburgh)
  • Annegret Burtscher (Radboud U)
  • Simone Calogero (CUT, Göteborg)
  • Piotr Chrušciel (U Vienna)
  • Roland Donninger (U Vienna)
  • David Fajman (U Vienna) — Organizer
  • Dietrich Häfner (UGA)
  • Jérémie Joudioux (MPIGP) — Organizer
  • Lavi Karp (Braude)
  • Mohammed Lemou (Université de Rennes 1)
  • Jonathan Luk (SU)
  • Maciej Maliborski (U Vienna)
  • Brien Nolan (DCU)
  • Todd Oliynyk (Monash U, Melbourne) — Organizer
  • Oliver Rinne (HTW Berlin)
  • Bernd Schmidt (MPIGP)
  • Walter Simon (U Vienna)
  • Jared Speck (Vanderbilt U, Nashville)
  • Robert Strain (Penn State)
  • Martin Taylor (Imperial College, London)
  • Juan Valiente-Kroon (QMU London)
  • Andras Vasy (SU)
  • Zoe Wyatt (U Cambridge)
At a glance
Thematic Programme
Feb. 1, 2021 -- March 12, 2021
ESI Boltzmann Lecture Hall
Håkan Andréasson (CUT, Göteborg)
David Fajman (U Vienna)
Jérémie Joudioux (MPIGP)
Todd Oliynyk (Monash U, Melbourne)