Rotating, stationary, axially symmetric spacetimes with collisionless matter

Abstract

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 ${\mathbb{R}}^5$.

29 pages. arXiv admin note: substantial text overlap with arXiv:1006.1225

References in corpus (3)

• The Einstein-Vlasov System/Kinetic Theory
• Existence of axially symmetric static solutions of the Einstein-Vlasov system
• Static self-gravitating elastic bodies in Einstein gravity

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