Spherical Universes with Anisotropic Pressure

Einstein’s equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the proper time, τ , experienced by the dust particles. The general solution contains four arbitrary functions of R M(R), L(R), E(R) and τ0(R). The solution is described by quadratures, which are in general elliptic integrals. It provides a generalization of the Lemâıtre-Tolman-Bondi solution. We present a discussion of the types of solution, and some examples. The relationship to Einstein clusters and the significance for gravitational collapse is also discussed. PACS numbers: 0420-q,0420Jb,9880Hw Submitted to: Class. Quantum Grav. Spherical Universes with Anisotropic Pressure 2