Static solutions of the spherically symmetric Vlasov-Einstein system. (English) Zbl 0806.35185
Summary: 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 centre and have isotropic or anisotropic pressure, and solutions which have a Schwarzschild-singularity at the centre.
MSC:
| 35Q75 | PDEs in connection with relativity and gravitational theory |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 85A05 | Galactic and stellar dynamics |
References:
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