Geometrical Structure in a Relativistic Thermodynamical Fluid Spacetime

Abstract

The goal of the present research paper is to study how a spacetime manifold evolves when thermal flux, thermal energy density and thermal stress are involved; such spacetime is called a thermodynamical fluid spacetime (TFS). We deal with some geometrical characteristics of TFS and obtain the value of cosmological constant Λ. The next step is to demonstrate that a relativistic TFS is a generalized Ricci recurrent TFS. Moreover, we use TFS with thermodynamic matter tensors of Codazzi type and Ricci cyclic type. In addition, we discover the solitonic significance of TFS in terms of the Ricci metric (i.e., Ricci soliton RS).

Keywords

• Lorentzian spacetime manifold
• Einstein’s field equation
• thermal energy momentum tensor
• curvatures
• Ricci solitons