Rotating relativistic stars: matching conditions and kinematical properties

Abstract

In the framework of general relativity, a description of the matching conditions between two rotating perfect fluids spacetimes in terms of the kinematical properties of the fluids is introduced. The Einstein and Darmois equations are written using coordinates adapted to the boundary separating both spacetimes. The functions appearing in the equations have an immediate physical interpretation. The analysis is extended to the case of matching a perfect fluid spacetime (star interior) with a vacuum spacetime (gravitational field outside the star). By solving a boundary problem for a first order partial differential equation (‘‘master equation’’) we define an exterior tetrad such that the matching conditions and the Einstein equations, for this case, reproduce those of the two-fluid problem. The formalism is applied to a particular static spherically symmetric star and to the Kerr metric.