On the physical properties of a nonquadratic solution for the McVittie metric

A particular class of McVittie's new nonquadratic solutions is examined with respect to its physical characteristics. It is found that center regularity is not compatible with negative pressure and density gradients. These solutions also have the strange geometric feature that the physical radius is a decreasing function of comoving radial coordinate. Models for nonstatic ''gaseous'' spheres (i.e., the density rho vanishes at the outer surface of the perfect fluid sphere together with the pressure p) have been constructed. The global motion is studied, and it has been found that pulsations are not possible. It is shown, however, that the density and pressure gradients are both negative. The pressure and the density are thus positive within the boundary of these ''gaseous'' spheres, and it is also seen that the density is increasing for contracting models. For the layers close to the outer boundary, it is shown that the pressure is increasing when the sphere is contracting. The speed of sound is thus real, and it is further seen that this speed is less than the speed of light. It is found that there exist bouncing models where the rate of change of circumference as measured by an observer riding on the boundary of the ''gaseous'' sphere is zero just at the moment when the sphere starts its reexpansion