Anistropic stars: Exact solutions and stability

I report on recent work concerning the existence and stability of self-gravitating spheres with anisotropic pressure. After presenting new exact solutions, Chandrasekhar's variational formalism for radial perturbations is generalized to anisotropic objects and applied to investigate their stability. It is shown that anisotropy can not only support stars of mass M and radius R with 2M/R greater than or equal to 8/9 and arbitrarily large surface redshifts, but that stable configurations exist for values of the adiabatic index gamma smaller than the corresponding isotropic value.