Communications in Mathematical Physics

, Volume 329, Issue 2, pp 787–808 | Cite as

Rotating, Stationary, Axially Symmetric Spacetimes with Collisionless Matter

  • Håkan Andréasson
  • Markus Kunze
  • Gerhard Rein


The existence of stationary solutions to the Einstein–Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat non-vacuum spacetimes. If angular momentum is allowed to be non-zero, the system of equations to solve contains one semilinear elliptic equation which is singular on the axis of rotation. This can be handled very efficiently by recasting the equation as one for an axisymmetric unknown on \({\mathbb{R}^5}\).


Angular Momentum Symmetric Function Implicit Function Theorem Bianchi Identity Total Angular Momentum 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Håkan Andréasson
    • 1
  • Markus Kunze
    • 2
  • Gerhard Rein
    • 3
  1. 1.Mathematical Sciences, Chalmers University of TechnologyGöteborg UniversityGöteborgSweden
  2. 2.Mathematisches InstitutUniversität KölnKölnGermany
  3. 3.Fakultät für Mathematik, Physik und InformatikUniversität BayreuthBayreuthGermany

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