  A review of the pseudo-complex General Relativity (pc-GR) is presented, with
the emphasis on observational consequences. First it is argued why to use an
algebraic extension and why the pseudo-complex is a viable one. Afterward, the
pc-GR is formulated. Posterior, several observational consequences are
discussed, as the perihelion shift of Mercury, Quasi Periodic Objects, the
emission profile of accretion discs, the pc-Robertson-Walker model of the
universe, neutron stars and gravitational ring-down modes of a black hole.
