Potentials in Energy Momentum Tensor and the Equation of State

In this letter we show that, abundant contents in the energy momentum tensor were overlooked and simply merged into the energy density ρ and pressure P . They are interactive potentials with different properties from that of ρ and P , which can be used as fingerprints for different interaction. In the usual treatment for particles moving in curved spacetime, the potential energy of the gravity seems to be ignored due to its subtle features. Via detailed calculation we find that, only T is independent variable, and all other thermodynamical variables together with these potentials can be expressed as some simple functions of T . Furthermore, these functions have little relationship with specific energy distribution function. PACS numbers: 95.30.Tg, 98.80.Jk, 64.30.+t, 05.20.-y