Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences , as well as the core-collapse of massive stars . We explore the stability of such disks against runaway and non-axisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the Thor code . We model the disk matter using the ideal fluid approximation with a \Gamma -law equation of state with \Gamma = 4 / 3 . We explore three disk models around non-rotating black holes with disk-to-black hole mass ratios of 0.24 , 0.17 and 0.11 . Due to metric blending in our initial data , all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations . Despite these oscillations , our models do not develop the runaway instability during the first several orbital periods . Instead , all of the models develop unstable non-axisymmetric modes on a dynamical timescale . We observe two distinct types of instabilities : the Papaloizou-Pringle and the so-called intermediate type instabilities . The development of the non-axisymmetric mode with azimuthal number m = 1 is accompanied by an outspiraling motion of the black hole , which significantly amplifies the growth rate of the m = 1 mode in some cases . Overall , our simulations show that the properties of the unstable non-axisymmetric modes in our disk models are qualitatively similar to those in Newtonian theory .