Some solutions of the Einstein field equations for a rotating perfect fluid

Abstract

The equations of isentropic rotational motion of a perfect fluid are investigated with use of Darboux’ theorem. It is shown that, together with the equation of continuity, they guarantee the existence of four scalar functions on space−time, which constitute a dynamically distinguished set of coordinates. It is assumed that in this coordinate system the metric tensor is constant along the lines tangent to velocity and vorticity fields. Under these assumptions a complete set of solutions of the field equations with Tij = (ε + p)uiuj − pgij is found. They divide into three families, first of which contains six types of new solutions with nonzero pressure. The second family contains only the Gödel’s solution, and the third one, only the Lanczos’ solution. Symmetry groups, exterior metrics, type of conformal curvature, geometrical and physical properties of the new solutions are investigated. A short review of other models of rotating matter is given.