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Taubs Variational Principle for Selfgravitating
A Hamiltonian Formalism for Selfgravitating
On the Hamiltonian Dynamics of Linear Perturbations
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canonical variables conjugate conservation of particle cosmological constant covariant derivative denotes density contrast function dp/dw eik'X Einstein field equations Einstein's theory energy density enthalpy per particle entropy per particle equations 3.2 equations of motion Euler-Lagrange equations explicitly fluid density perturbations fluid is isentropic fluid obeys fluid vorticity perturbations formalism for self-gravitating four-velocity FRW spacetime gravitational wave perturbations h UQ Hamiltonian dynamical Hamiltonian formalism Hamiltonian variational integral Hamiltonlan variational principle isentropic perfect fluid Jd3k elk'X junction conditions Lagrange multiplier lapse function line element 4.1 linear perturbation theory method of second metric tensor Moncrief obeys an equation odd parity linear Oppenheimer-Snyder spacetimes parity linear perturbations particle number perturbations defined perturbations of Oppenheimer-Snyder radiation restricted comoving coordinates second fundamental forms second variation self-gravitating isentropic perfect self-gravitating perfect fluid shift vector field spacelike surface spacetime metric spherical harmonics spherically symmetric spin weight supplementary variables Taub's variational variables h vorticity tensor wave equation