A new solution for a rotating perfect fluid in general relativity

A new exact solution of Einstein's field equations with the energy-momentum tensor of a perfect fluid is given. This solution can be interpreted as a stationary axisymmetric gravitational field which is regular and satisfies the dominant energy condition everywhere inside a closed surface of vanishing pressure. The fluid rotates rigidly; the equation of state is epsilon +3p=constant. The solution is of Petrov type D and admits a maximal group G₂ of motions.