Thermodynamic Functions of the Universe in the Presence of Viscosity in the Relativity Theory and Lyra Geometry

Abstract

: This paper investigates the thermodynamic functions of the universe in the presence of viscous fluid in general relativity and Lyra geometry. The space-time is modeled by Bianchi type 𝑉𝐼 0 cosmological model. The field equations' solution is obtained considering that the scalar expansion θ of the cosmological model is proportional to the eigenvalue 𝜎 11 of the shear tensor 𝜎 𝑖𝑗 . The thermodynamic functions are studied for the universe and their values are compared in general relativity and Lyra geometry. For all obtained models, the entropy is consistent with the second law of thermodynamics. The physical and geometrical properties of the obtained models are discussed. Also, we show that the Lyra term 𝛽 plays the role of the variable cosmological term in the relativity theory and can not be identified as a viscosity term. Without the viscosity term, we obtain the entropy as a constant 𝑺 = constant. That is the universe is in an adiabatic state. The Bianchi type 𝑉𝐼 0 cosmological model presented in this paper explains a stage of evolution with the positive deceleration parameter.