A review on algebraic extensions in general relativity

A brief review on algebraic extensions of general relativity is presented. After a short summary of first attempts by Max Born and Albert Einstein, all possible algebraic extensions will be discussed, with the pseudo-complex (pc) extension left as the only viable one, because it does not contain ghost solutions. Also some metric extensions are presented, such as the non-symmetric gravitation theory and the Finsler metric. Some predictions of the pc extension are discussed, such as the structure of light emission of an accretion disk around a black hole, the redshift at the surface of a compact star as a function in the azimuthal angle, and whether there is an upper limit for the mass of a neutron star.