Abstract:
The Vlasov–Poisson and Vlasov–Einstein systems model the motion of a self gravitating system such as a galaxy. The Vlasov–Poisson system is nonrelativistic. Jeans' theorem states that every spherically symmetric solution of the Vlasov–Poisson system that is independent of time may be expressed as a function of the two invariants, energy and angular momentum. This paper shows this is not the case for the Vlasov–Einstein system.
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Received: 2 November 1998 / Accepted: 24 December 1998
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Schaeffer, J. A Class of Counterexamples to Jeans' Theorem for the Vlasov–Einstein System. Comm Math Phys 204, 313–327 (1999). https://doi.org/10.1007/s002200050647
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DOI: https://doi.org/10.1007/s002200050647