Hamiltonian structure of the Vlasov-Einstein system and the problem of stability for spherical relativistic star clusters
- Florida Univ., Gainesville, FL (United States)
- Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
The Hamiltonian formulation of the Vlasov-Einstein system, which is appropriate for collisionless, self-gravitating systems like clusters of stars that are so dense that gravity must be described by the Einstein equation, is presented. In particular, it is demonstrated explicitly in the context of a 3 + 1 splitting that, for spherically symmetric configurations, the Vlasov-Einstein system can be viewed as a Hamiltonian system, where the dynamics is generated by a noncanonical Poisson bracket, with the Hamiltonian generating the evolution of the distribution function f (a noncanonical variable) being the conserved ADM mass-energy H{sub ADM}. An explicit expression is derived for the energy {delta}({sup 2})H{sub ADM} associated with an arbitrary phase space preserving perturbation of an arbitrary spherical equilibrium, and it is shown that the equilibrium must be linearly stable if {delta}({sup 2})H{sub ADM} is positive semi-definite. Insight into the Hamiltonian reformulation is provided by a description of general finite degree of freedom systems.
- Research Organization:
- Univ. of Texas, Austin, TX (United States). Institute for Fusion Studies
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG05-80ET53088
- OSTI ID:
- 10120708
- Report Number(s):
- DOE/ET/53088-585; IFSR-585; ON: DE93006180
- Resource Relation:
- Other Information: PBD: Nov 1992
- Country of Publication:
- United States
- Language:
- English
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