Math. Proc. Camb. Phil. Soc. 115, 559 - 570 (1994)
Static solutions of the spherically symmetric
Vlasov-Einstein system
G. Rein
We consider the Vlasov-Einstein system in a
spherically symmetric setting
and prove the existence of static solutions
which are asymptotically flat and
have finite total mass and finite extension of the matter.
Among these there
are smooth, singularity-free solutions, which have a regular center and may
have isotropic or anisotropic pressure, and also solutions, which have a
Schwarzschild-singularity at the center.
The paper is an extension of previous
work, where only smooth,
globally defined solutions with regular center and
isotropic pressure were considered, cf.
Rein, G., Rendall, A.: Smooth static solutions of the spherically symmetric
Vlasov-Einstein system.
Ann. de l'Inst. H. Poincaré, Physique Théorique 59,
383 - 397 (1993)
Gerhard Rein (rein@rz.mathematik.uni-muenchen.de)