Burlykov V. Perfect fluid spheres in general relativity

The work is concerned with exact analytical solutions to Einstein field equations representing spherically symmetric distributions of matter in general relativity. The nonstatic model of the uniform - density distribution of matter represented by a perfect fluid is investigated. The fluid sphere is assumed to be bounded by empty space. The physical properties of the general solution are studied. All the possible types of the evolution for a large class of the models are found. Three new specific models are con-structed and investigated. A number of new uniform - density solutions for anisotropic fluid spheres (static and nonstatic) are derived and investigated. New static solutions for anisotropic fluid spheres with the linear mass function are derived and studied. The derived solutions are matched to the empty space.