In this work, we investigate the validity of the GSL of thermodynamics in the universe (open, closed and flat) governed by Hořava–Lifshitz (HL) gravity. If the universe contains barotropic fluid, we obtain the corresponding solutions. The validity of the GSL is examined by two approaches: (i) the robust approach and (ii) the effective approach. In the robust approach, we consider that the universe contains only matter fluid. Also, the effect of the gravitational sector of HL gravity is incorporated through the modified black hole entropy on the horizon. The effective approach is that all extra information of HL gravity is cast into an effective dark energy fluid, and so we consider that the universe contains matter fluid plus this effective fluid. This approach is essentially the same as Einstein's gravity theory. The general prescription for the validity of the GSL is discussed. Graphically, we show that the GSL may be satisfied for the open, closed and flat universes on the different horizons with different conditions.
Validity of Thermodynamical Laws in Dark Energy Filled Universe