Anisotropic spheres admitting a one-parameter group of conformal motions

The Einstein equations for spherically symmetric distributions of anisotropic matter (principal stresses unequal), are solved, assuming the existence of a one-parameter group of conformal motions. All solutions can be matched with the Schwarzschild exterior metric on the boundary of matter. Two families of solutions represent, respectively, expanding and contracting spheres which asymptotically tend to a static sphere with a surface potential equal to (1)/(3) . A third family of solutions describes ‘‘oscillating black holes.’’ All solutions possess a positive energy density larger than the stresses everywhere.