Hamiltonian formulation of the linearized perturbation equations for the Vlasov-Einstein system of relativistic stellar dynamics

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Abstract

Relativistic star clusters are often modeled as static, spherically symmetic solutions to the Vlasov-Einstein system. It is shown here that, for spherical disturbances, the equations for linearized perturbations about such a static equilibrium can be cast into a Hamiltonian form using relativistic analogues of Morrison's bracket for the Vlasov-Poisson system and the energy functional of Lynden-Bell and Sanitt for a linearized perturbation.

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