Collapsing void in an expanding universe

Abstract

We consider here the model of a spherical void in an expanding Robertson - Walker (RW) universe with flat space sections. The void is taken as a sphere of low density conducting perfect fluid (Region I) surrounded by a spherical shell of pure radiation (Region II). The metric in Region I is assumed to be special form of the solution of Maiti (1982) and that in Region II is that of Vaidya. The RW universe (Region III) surrounding the above combination is assumed to be filled with a perfect fluid having a linear equation of state so that the scale factor is given by t to the power n. The matching conditions are written down and solved. The arrow of time shows that the void appears to contract when seen by a comoving observer in the RW universe. It, however, the RW universe is filled up with dust (P=0), then the void remains static and the Vaidya metric reduces to that of Scwarzchild. The co-ordinates of Region II are extended to Regions I and III.