Vlasov equation and collisionless hydrodynamics adapted to curved spacetime

Dodin, I. Y.; Fisch, N. J.
November 2010
Physics of Plasmas;Nov2010, Vol. 17 Issue 11, p112118
Academic Journal
The modification of the Vlasov equation, in its standard form describing a charged particle distribution in the six-dimensional phase space, is derived explicitly within a formal Hamiltonian approach for arbitrarily curved spacetime. The equation accounts simultaneously for the Lorentz force and the effects of general relativity, with the latter appearing as the gravity force and an additional force due to the extrinsic curvature of spatial hypersurfaces. For an arbitrary spatial metric, the equations of collisionless hydrodynamics are also obtained in the usual three-vector form.


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