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Thermodynamical Laws in Horava-Lifshitz Gravity

In this work, we have investigated the validity of GSL of thermodynamics in a universe (open, closed and flat) governed by Ho$\check{\text r}$ava-Lifshitz gravity. If the universe contains barotropic fluid the corresponding solutions have been obtained. The validity of GSL have been examined by two approaches: (i) robust approach and (ii) effective approach. In robust approach, we have considered the universe contains only matter fluid and the effect of the gravitational sector of HL gravity was incorporated through the modified black hole entropy on the horizon. Effective approach is that all extra information of HL gravity into an effective dark energy fluid and so we consider the universe contains matter fluid plus this effective fluid. This approach is essentially same as the Einstein's gravity theory. The general prescription for validity of GSL have been discussed. Graphically we have shown that the GSL may be satisfied for open, closed and flat universe on the different horizons with different conditions.