Two fluid acoustic modes and inhomogeneous cosmologies

Abstract

The weak discontinuities that can propagate in a relativistic two fluid system are examined and expressions obtained for their speed of propagation. The acoustic speeds and discontinuity amplitudes are described by their Frenet parameters. Both longitudinal and transverse acoustic modes are possible. The discontinuity in the two fluid anisotropy vector can be timelike, spacelike, or null. As an application we use the existence of two longitudinal modes to extend the fluid content of the inhomogeneous cosmologies discussed by Van den Bergh and Skea(1993). For their solution we find a family of two perfect fluids whose properties range from a dust-perfect-fluid set to two gamma =4/3 comoving perfect fluids.