TRAPPED SURFACES IN CLOSED FRIEDMANN UNIVERSES

Explicit expressions for the location of cosmological trapped surfaces in closed Friedmann-type universes dominated by matter with an equation of state of the form p=(γ-1)ρ, γ>2/3, are obtained. Physically important cases of pressureless matter (γ=1), radiation (γ=4/3), a massless scalar field (γ=2), and a decoupled mixture of matter and radiation are considered. Penrose diagrams for these special cases are drawn, showing the location of trapped and marginally trapped surfaces. It is demonstrated by means of counterexamples that current classification schemes fail to properly distinguish between trapping horizons of cosmological versus noncosmological origin. © 1995 The American Physical Society.