Second law of gravitational thermodynamics in the locally rotationally symmetricBianchi type-II universe

Abstract

In this work, under the assumption that the universe is locally rotationally symmetric (LRS) Bianchi type-IIand lled with anisotropic dark uid (dark energy and dark radiation), we investigate whether the generalized secondlaw of thermodynamics (GSLT) is still valid. We also consider another important condition for LRS Bianchi type-IIspacetimes whereby the model expansion is proportional to the shear , which leads toB=An(where n is a constantand A and B are the metric potentials). Based on this, we derive a general circumstance for the GSLT and nd that itsvalidity depends on the anisotropies of both the dark uid and the metric potentials. We conclude that the GSLT stillholds at all times even if these two anisotropic conditions are removed from the results.