Numerical construction of cosmological black holes in a generalized Lemaitre-Tolman-Bondi model with pressure

We study the evolution of some simple cosmological black holes in the framework of the generalized Lemaitre-Tolman-Bondi (LTB) model developed by Lasky and Lun, which includes the effects of nonzero pressure. A small Gaussian overdensity is introduced into the LTB solutions, and an equation of state is assumed in order to fix the relation between the pressure and the density. Numerical solutions are calculated, which simulate the dynamical effects of the pressure field on the formation of a black hole as the end state of the collapse. The influence of the pressure effects on the behavior of the solutions is measured by comparing the development of the generalized LTB model with that of the corresponding pressure-free LTB model. Finally, we plot the location of the apparent horizon on each shell and examine the differences in the locations between the cases with and without pressure. The evidence indicates that the apparent horizon forms later in the presence of pressure.