Hamiltonian structure of the Vlasov-Einstein system and the problem of stability for spherical relativistic star clusters [electronic resource].
- Published
- Washington, D.C. : United States. Dept. of Energy, 1992.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy. - Physical Description
- Pages: (73 pages) : digital, PDF file
- Additional Creators
- University of Texas at Austin, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
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- Free-to-read Unrestricted online access
- Summary
- 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.
- Report Numbers
- E 1.99:doe/et/53088-585
E 1.99: ifsr--585
ifsr--585
doe/et/53088-585 - Subject(s)
- Other Subject(s)
- Note
- Published through SciTech Connect.
11/01/1992.
"doe/et/53088-585"
" ifsr--585"
"DE93006180"
Morrison, P.J. . Inst. for Fusion Studie; Kandrup, H.E. - Funding Information
- FG05-80ET53088
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