We investigate the consequences of the pseudo-complex General Relativity within a pseudo-complexified Roberston-Walker metric. A contribution to the energy-momentum tensor arises, which corresponds to a dark energy and may change with the radius of the universe, i.e., time. Only when the Hubble function H does not change in time, the solution is consistent with a constant Λ.

The pseudo-complex extension of general relativity will be reviewed, and as a special case the pseudo-complex Schwarzschild metric will be discussed. As a consequence of the pseudo-complex extension, dark energy which accumulates around central mass concentrations arises. The collapse of a large mass will be avoided due to the presence of dark energy. Some experimental consequences will be discussed, like the redshift around large mass concentrations and the perihelion shift of Mercury.

In this paper, the effects of a minimal length are investigated within an algebraically extended theory of General Relativity (GR). Former attempts, to include a minimal length in GR, are first resumed with a conformal factor of the metric as a consequence. Effective potentials for various black hole masses (as ratios to the minimal length) are deduced. It is found that the existence of a minimal length has, for a small mass black hole, important effects on the effective potential near the event horizon, creating barriers which inhibit that particles can pass the event horizon. Further, a new limit for the minimal mass of a black hole is derived.