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Neutrino transport and neutrino-matter interactions are known to play animportant role in the evolution of neutron star mergers, and of theirpost-merger remnants. Neutrinos cool remnants, drive post-merger winds, anddeposit energy in the low-density polar regions where relativistic jets mayeventually form. Neutrinos also modify the composition of the ejected material,impacting the outcome of nucleosynthesis in merger outflows and the propertiesof the optical/infrared transients that they power (kilonovae). So far, mergersimulations have largely relied on approximate treatments of the neutrinos(leakage, moments) that simplify the equations of radiation transport in a waythat makes simulations more affordable, but also introduces unquantifiableerrors in the results. To improve on these methods, we recently published afirst simulation of neutron star mergers using a low-cost Monte-Carlo algorithmfor neutrino radiation transport. Our transport code limits costs in opticallythick regions by placing a hard ceiling on the value of the absorption opacityof the fluid, yet all approximations made within the code are designed tovanish in the limit of infinite numerical resolution. We provide here anin-depth description of this algorithm, of its implementation in the SpECmerger code, and of the expected impact of our approximations in opticallythick regions. We argue that the latter is a subdominant source of error at theaccuracy reached by current simulations, and for the interactions currentlyincluded in our code. We also provide tests of the most important features ofthis code.

Implementation of Monte-Carlo transport in the general relativistic SpEC code