Numerical Evolution of General Relativistic Voids

Abstract

In this paper, we study the evolution of a relativistic, superhorizon-sized void embedded in a Friedmann-Robertson-Walker universe. We numerically solve the spherically symmetric general relativistic equations in comoving, synchronous coordinates. Initially, the fluid inside the void is taken to be homogeneous and nonexpanding. In a radiation- dominated universe, we find that radiation diffuses into the void at approximately the speed of light as a strong shock---the void collapses. We also find the surprising result that the cosmic collapse time (the $1^{\rm st}$-crossing time) is much smaller than previously thought, because it depends not only on the radius of the void, but also on the ratio of the temperature inside the void to that outside. If the ratio of the initial void radius to the outside Hubble radius is less than the ratio of the outside temperature to that inside, then the collapse occurs in less than the outside Hubble time. Thus, superhorizon-sized relativistic void may thermalize and homogenize relatively quickly. These new simulations revise the current picture of superhorizon-sized void evolution after first-order inflation.Comment: 37 pages plus 12 figures (upon request-- [email protected]) LaTeX, FNAL-PUB-93/005-