Thermodynamical Laws in Horava-Lifshitz Gravity

TL;DR

This paper examines the validity of the generalized second law of thermodynamics in universes governed by Hořava-Lifshitz gravity, considering different approaches and universe geometries, and finds conditions under which GSL holds.

Contribution

It introduces two approaches to test GSL in Hořava-Lifshitz gravity and analyzes their validity across different universe geometries and horizons.

Findings

GSL can be satisfied in open, closed, and flat universes under certain conditions.

The effective approach aligns with Einstein's gravity, simplifying analysis.

Graphical results support the validity of GSL in various scenarios.

Abstract

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.