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Neutrino-matter interactions play an important role in the post-mergerevolution of neutron star-neutron star and black hole-neutron star mergers.Most notably, they determine the properties of the bright optical/infraredtransients observable after a merger. Unfortunately, Boltzmann's equations ofradiation transport remain too costly to be evolved directly in mergersimulations. Simulations rely instead on approximate transport algorithms withunquantified modeling errors. In this paper, we use for the first time atime-dependent general relativistic Monte-Carlo (MC) algorithm to solveBoltzmann's equations and estimate important properties of the neutrinodistribution function ~10ms after a neutron star merger. We do not fully couplethe MC algorithm to the fluid evolution, but use a short evolution of themerger remnant to critically assess errors in our approximate gray two-momenttransport scheme. We demonstrate that the analytical closure used by the momentscheme is highly inaccurate in the polar regions, but performs well elsewhere.While the average energy of polar neutrinos is reasonably well captured by thetwo-moment scheme, estimates for the neutrino energy become less accurate atlower latitudes. The two-moment formalism also overestimates the density ofneutrinos in the polar regions by ~50%, and underestimates the neutrinopair-annihilation rate at the poles by factors of 2-3. Although the latter issignificantly more accurate than one might have expected before this study, ourresults indicate that predictions for the properties of polar outflows and forthe creation of a baryon-free region at the poles are likely to be affected byerrors in the two-moment scheme, thus limiting our ability to reliably modelkilonovae and gamma-ray bursts.

Evaluating radiation transport errors in merger simulations using a Monte-Carlo algorithm