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If one assumes a particular form of non-minimal coupling, called the conformal coupling, of a perfect fluid with gravity in the fluid-gravity Lagrangian then one gets modified Einstein field equation. In the modified Einstein equation the effect of the non-minimal coupling does not vanish if one works with spacetimes for which the Ricci scalar vanishes. In the present work we use the Schwarzschild metric in the modified Einstein equation, in the presence of non-minimal coupling with a fluid, and find out the energy-density and pressure of the fluid. In the present case the perfect fluid is part of the solution of the modified Einstein equation. We also solve the modified Einstein equation, using the flat spacetime metric and show that in the presence of non-minimal coupling one can accommodate a perfect fluid of uniform energy-density and pressure in the flat spacetime. In both the cases the fluid pressure turns out to be negative. Except these non-trivial solutions it must be noted that the vacuum solutions also remain as trivial valid solutions of the modified Einstein equation in the presence of non-minimal coupling. [ABSTRACT FROM AUTHOR]

A non-equilibrium thermodynamic analysis has been done for the interacting dark fluid in the universe bounded by the event horizon. From observational evidences it is assumed that at present the matter in the universe is dominated by two dark sectors-dark matter and dark energy (DE). The mutual interaction among them results in spontaneous heat flow between the horizon and the fluid system and the thermal equilibrium will no longer hold. In the present work, the dark matter is chosen in the form of dust while the DE is chosen as a perfect fluid with constant equation of state in one case and holographic DE model is chosen in the other. Finally, validity of the generalized second law of thermodynamics has been examined in both cases. [ABSTRACT FROM AUTHOR]