Slowly rotating fluid spheres in general relativity with and without radiation

We introduce slow rotation to some of the solutions given by Vaidya, which correspond to radiating fluid spheres in general relativity. We give several new analytic solutions, some of which correspond to uniform rotation and others to differentially rotating fluid spheres. We also study the stationary field equations for slowly rotating and nonradiating fluid spheres, and present a new analytic solution and also generalize the solution corresponding to the $P=\alpha \rho$ equation of state. Some of the solutions mentioned above could be physically reasonable throughout the star while the rest could be used to represent portions of it. We discuss the physical properties of these solutions and the boundary conditions in detail.