Pressure in Lema\^{i}tre-Tolman-Bondi solutions and cosmologies

Lema\^{i}tre-Tolman-Bondi (LTB) solutions have traditionally been confined to systems with no pressure in which the gravity is due to massive dust, but the solutions are little changed in form if, as in cosmology, the pressure is uniform in space at each comoving time. This allows the equations of cosmology to be deduced in a manner that more closely resembles classical mechanics. It also gives some inhomogeneous solutions with growing condensations and black holes. We give criteria by which the sizes of different closed models of the universe can be compared and discuss conditions for self-closure of inhomogeneous cosmologies with a $\Lambda$-term.