The Rest-Frame Instant Form of Relativistic Perfect Fluids and of Non-Dissipative Elastic Materials

For perfect fluids with equation of state $\rho = \rho (n,s)$, Brown gave an action principle depending only on their Lagrange coordinates $\alpha^i(x)$ without Clebsch potentials. After a reformulation on arbitrary spacelike hypersurfaces in Minkowski spacetime, the Wigner-covariant rest-frame instant form of these perfect fluids is given. Their Hamiltonian invariant mass can be given in closed form for the dust and the photon gas. The action for the coupling to tetrad gravity is given. Dixon's multipoles for the perfect fluids are studied on the rest-frame Wigner hyperplane. It is also shown that the same formalism can be applied to non-dissipative relativistic elastic materials described in terms of Lagrangian coordinates.Comment: revtex file, 70 page

Analytical and numerical properties of Q-balls

Stable non-topological solitons, Q-balls, are studied using analytical and numerical methods. Three different physically interesting potentials that support Q-ball solutions are considered: two typical polynomial potentials and a logarithmic potential inspired by supersymmetry. It is shown that Q-balls in these potentials exhibit different properties in the thick-wall limit where the charge of a Q-ball is typically considerably smaller than in the thin-wall limit. Analytical criteria are derived to check whether stable Q-balls exists in the thick-wall limit for typical potentials. Q-ball charge, energy and profiles are presented for each potential studied. Evaporation rates are calculated in the perfect thin-wall limit and for realistic Q-ball profiles. It is shown that in each case the evaporation rate increases with decreasing charge.Comment: 25 page