On the equations of state for irrotational perfect fluid in general relativity

Equations of state for an irrotational perfect fluid are investigated. It is shown that the equations of state in the form: a) rho = const, P not equal to const, b) P = const, rho,sub(k) = rho,sub(n)usup(n)usub(k) not equal to 0, c) P,sub(k) = P,sub(n)usup(n)usub(k), rho,sub(k) = rho,sub(n)usup(n)usub(k), d) rho,sub(k) = αP,sub(k), rhosub(n)usup(n) = P,sub(n)usup(n) = 0 do not contradict the Einstein field equations. Finally we present the physically realistic equations of state. (author)