Evolving Hořava cosmological horizons

Several sets of radially propagating null congruence generators are exploited in order to form 3-dimensional marginally trapped surfaces, referred to as black hole and cosmological apparent horizons in a Hořava universe. Based on this method, we deal with the characteristics of the 2-dimensional space-like spheres of symmetry and the peculiarities of having trapping horizons. Moreover, we apply this method in standard expanding and contracting FLRW cosmological models of a Hořava universe to investigate the conditions under which the extra parameters of the theory may lead to trapped/anti-trapped surfaces both in the future and in the past. We also include the cases of negative time, referred to as the finite past, and discuss the formation of anti-trapped surfaces inside the cosmological apparent horizons.