Unified first law in inhomogeneous and anisotropic spacetime models: Some general prescription

In this paper we investigate the interrelationship between the unified first law of thermodynamics and the Friedmann equations for three anisotropic and inhomogeneous spacetime metrics namely Lemaître–Tolman–Bondi and Friedmann–Lemaître–Robertson–Walker type inhomogeneous spacetime model and Kantowski–Sachs type model. In all these models we find that Einstein field equations are obtained by projecting the unified first law along and perpendicular to the Kodama vector and also along two linearly independent directions.