Observational Tests of the Pseudo-complex Theory of GR Using Black Hole Candidates

Abstract

We have worked out astronomical tests of the pseudo-complex gravitational field theory (pc-GR) proposed by Hess and Greiner [1] going beyond our first paper on pc-GR tests [2]. Observational tests of the standard GR theory (standard-GR) and the pc-GR theory include (i) Galactic binaries, (ii) the Galactic Center, and (iii) supermassive black holes. For Galactic binaries with both relativistic Fe K line emission and QPO frequencies we have calculated the distances of both observational quantities to the central black hole. While the relativistic Fe K emission arises only within a few gravitational radii (\(R_G = GM/c^2\)) from the black hole with mass M, the QPO frequencies when related to Keplerian motions place their origin to much larger distances. This discrepancy is not understood so far. As very little has been done going beyond the phenomenological description of that problem, we applied the pseudo-complex theory to these Galactic black hole binaries and find that the Fe K and QPO emission is arising at quite similar radii from the black hole. While this is not any proof for the pc-GR, it is worth pointing out that both theories give different results. For the Galactic Center we show that the orbital frequencies of test particles are different in pc-GR and standard GR. In addition, we show that VLBI interferometry will result into the first direct image of the black hole in the GC and that ray-tracing images in both theories are different for the GC and can be used to probe standard GR and pc-GR. Finally, we argue that in supermassive black holes the QPO frequencies and the relativistic Fe K emission occur from the same physical origin. This further allows performing tests on pc-GR and standard GR from both observational quantities.