The pseudo-complex General Relativity (pc-GR) is further considered. A new projection method is proposed. It is shown, that the pc-GR introduces automatically terms into the system which can be interpreted as dark energy. The modified pseudo-complex Schwarzschild solution is investigated. The dark energy part is treated as a liquid and possible solutions are discussed. As a consequence, the collapse of a large stellar mass into a singularity at r = 0 is avoided and no event-horizon is formed. Thus, black holes don't exist. The resulting object can be viewed as a gray star. It contains no singularity which emphasizes, again, that it is not a black hole For the latter, a special solution is presented. Finally, we will consider the orbital speed of a mass in a circular orbit and suggest a possible experimental verification.

Motivated by possible observations of the black hole candidate in the center of our galaxy (Gillessen et al., 2012;Eisenhauer et al., 2011) and the galaxy M87 (Doeleman et al., 2009;Falcke et. al, 2012), ray-tracing methods are applied to both standard General Relativity (GR) and a recently proposed extension, the pseudo-complex General Relativity (pc-GR). The correction terms due to the investigated pc-GR model lead to slower orbital motions close to massive objects. Also the concept of an innermost stable circular orbit (ISCO) is modified for the pc-GR model, allowing particles to get closer to the central object for most values of the spin parameter a than in GR. Thus, the accretion disk, surrounding a massive object, is brighter in pc-GR than in GR. Iron Kα emission line profiles are also calculated as those are good observables for regions of strong gravity. Differences between the two theories are pointed out.

Based on previous publications exploring pseudo-complex General Relativity (pc-GR) we present a selection of observable consequences of pc-GR and possible ways to experimentally access them. Whenever possible we compare the results to Einstein's GR and differences are worked out in detail. We propose experimental tests to check the predictions of pc-GR for the orbital frequency of test particles, the gravitational redshift effect and the last stable orbit. We will show that the orbital frequency of test particles at a given radius in pc-GR is in general lower compared to standard GR. Also the effect of frame dragging is modified (weakened) in pc-GR. Concerning the gravitational redshift of a radiation emitting object we find that it is also lower in pc-GR than in standard GR. Eventually the classical concept of a last stable orbit has to be modified in pc-GR. arXiv:1209.2815v2 [gr-qc]