Peculiar velocities of nonlinear structure: Voids in McVittie spacetime

As a study of peculiar velocities of nonlinear structure, we analyze the mo del of a relativistic thin-shell void in the expanding universe. First, ado pting McVittie (MV) spacetime as a background universe, we investigate the dynamics of an uncompensated void with negative MV mass. Although the motio n itself is quite different from that of a compensated void, as shown by Ha ines & Harris, the present peculiar velocities are not affected by MV mass. Second, we discuss how precisely the formula in the linear perturbation th eory applies to nonlinear relativistic voids, using the results of our firs t investigation as well as previous results for the homogeneous background (Sakai, Maeda, & Sate). Third, we reexamine the effect of the cosmic microw ave background radiation. Contrary to the results of Pim & Lake, we find th at the effect is negligible. We show that their results are due to inapprop riate initial conditions. Our results in the three parts of our study sugge st that the formula in the linear perturbation theory is approximately vali d even for nonlinear voids.