We discuss the relevance of the exact solutions to the Einstein equations in the development of general relativity, in particular the solutions with axial symmetry. We present a summary of the Newtonian gravity theory with emphasis in the generation of solutions to the Poisson equation that represent disks. Also the Rayleigh criterion of stability is discussed in this context. We give a summary of the Einstein theory of gravitation and present the Weyl solution that represent the gravitational field of a body with axial symmetry. The generation of exact solutions to the Einstein equations that describe the space-time associated to thin disks, thick disks and disks with halos is studied using an extention of the image method. The physical parameters of the disks such as, density, pressure, sound velocity are also analyzed in detail. Furthermore, both the Rayleigh stability and hydrodynamical stability are studied for a family of thin isotopic disks previously studied.
axial symmetry; disks; stability; black holes; exact solutions; Einstein equations
