The merger of two neutron stars (NSs) or a neutron star and a black hole (BH) produces a radioactively-powered transient known as a kilonova, first observed accompanying the gravitational wave event GW170817. While kilonovae are frequently modeled in spherical symmetry, the dynamical ejecta and disk outflows can be considerably asymmetric. We use Monte Carlo radiative transfer calculations to study the light curves of kilonovae with globally axisymmetric geometries (e.g. an ellipsoid and a torus). We find that the variation in luminosity in these models is most pronounced at early times, and decreases until the light curves become isotropic in the late optically thin phase. The light curve shape and peak time are not significantly modified by the global asymmetry. We show that the projected surface area along the line of sight captures the primary geometric effects, and use this fact to provide a simple analytic estimate of the direction-dependent light curves of the aspherical ejecta. For the kilonova accompanying GW170817, accounting for asymmetry with an oblate (prolate) ellipsoid of axial ratio $2$ ($1/2$) leads to a $sim 40 %$ decrease (increase) in the inferred ejecta mass compared to the spherical case. The pole-to-equator orientation effects are expected to be significantly larger (a factor of $sim 5 - 10$) for the more extreme asymmetries expected for some NS-BH mergers.
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