  One viable seeding mechanism for supermassive black holes is the direct
gaseous collapse route in pre-galactic dark matter halos, producing objects on
the order of $10^4 - 10^6$ solar masses. These events occur when the gas is
prevented from cooling below $10^4$ K that requires a metal-free and relatively
H$_2$-free medium. The initial collapse cools through atomic hydrogen
transitions, but the gas becomes optically thick to the cooling radiation at
high densities. We explore the effects ofLyman-$\alpha$ trapping in such a
collapsing system with a suite of Monte Carlo radiation transport calculations
in uniform density and isotropic cases that are based from a cosmological
simulation. Our method includes both non-coherent scattering and two-photon
line cooling. We find that Lyman-$\alpha$ radiation is marginally trapped in
the parsec-scale gravitationally unstable central cloud, allowing the
temperature to increase to 50,000 K at a number density of $3 \times 10^4$
cm$^{-3}$ and increasing the Jeans mass by a factor of five. The effective
equation of state changes from isothermal at low densities to have an adiabatic
index of 4/3 around the temperature maximum and then slowly retreats back to
isothermal at higher densities. Our results suggest that Lyman-$\alpha$
trapping delays the initial collapse by raising the Jeans mass. Afterward the
high density core cools back to $10^4$ K that is surrounded by a warm envelope
whose inward pressure may alter the fragmentation scales at high densities.
