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Numerous cosmological simulations have been performed to study the formation of the first objects. We present the results of high‐resolution 3D cosmological simulations of the formation of primordial objects using the adaptive mesh refinement code  flash  by including in an approximate manner the radiative transfer effects of Lyman α photons. We compare the results of a Lyman α trapping case inside gas clouds with atomic and molecular hydrogen cooling cases. The principal objective of this research is to follow the collapse of a zero metallicity halo with an effective equation of state (that accounts for the trapping) and to explore the fate of a halo in each of the three cases, specifically the impact of thermodynamics on the fragmentation of haloes. Our results show that in the case of Lyman α trapping, fragmentation is halted and a massive object is formed at the centre of a halo. The temperature of the gas remains well above 10 4  K and the halo is not able to fragment to stellar masses. In the atomic cooling case, gas collapses into one or two massive clumps in contrast to the Lyman α trapping case. For the molecular hydrogen cooling case, gas cools efficiently and fragments. The formation of massive primordial objects is thus strongly dependent on the thermodynamics of the gas. A salient feature of our results is that for the formation of massive objects, e.g. intermediate‐mass black holes, feedback effects are not required to suppress  H 2   cooling, as molecular hydrogen is collisionally dissociated at temperatures higher than 10 4  K as a consequence of Lyman α trapping.

The impact of Lyman α trapping on the formation of primordial objects