Predictions of the pseudo-complex theory of Gravity for EHT observations – II: theory and predictions

Abstract

We present a resumé on the modified theory of gravity, called pseudo-complex General Relativity (pc-GR). It is the second in a series of papers, where the first one (Boller et al. 2019, referred to as paper I) discussed the observational consequences of pc-GR. In this paper, we concentrate on the underlying theory. PC-GR involves an algebraic extension of the standard theory of GR and it depends on two phenomenological parameters. An element included in pc-GR that is not present in standard GR is the energy-momentum tensor corresponding to an anisotropic ideal fluid, which we call dark energy. The two parameters are related to the coupling of mass to the dark energy and its fall-off as a function of r. The consequences and predictions of this theory will be discussed in the context of the observational results of the Even Horizon Telescope, expected soon. Our main result is that due to the accumulation of dark energy near a large mass, the modified theory predicts a dark ring followed by a bright ring in the emission profile of the accretion disc. We also discuss the light ring in the equatorial plane.

Kerr Black Holes within a Modified Theory of Gravity

“…The theory predicts a different behavior of an accretion disc near the black hole, showing a dark ring followed by a bright one further in. Studies on this were also published in [14,15] and more recently in [16,17]. The main feature is the ring structure, mentioned above, which is quite independent from the mass of the black hole and the type of the accretion disc (if it is thin, thick, a torus, .…”

“…with the metric components listed in (17). Circular orbital motion is defined byṙ = dr dτ = 0, where dτ is either the infinitesimal difference of the eigentime or the length element dω.…”

“…Circular orbital motion is defined byṙ = dr dτ = 0, where dτ is either the infinitesimal difference of the eigentime or the length element dω. The particle moves on a geodesic path and the deduced frequency is given by [17]…”

Comparison of the predictions of the pseudocomplex general relativity to the observations of the Event Horizon Telescope collaboration

“…The intention of our contribution is to compare some of the results to the ones of an extended theory of gravity (Hess et al ; Hess & Greiner , ), which will be given in Section 2. In two recent publications (Boller et al ; Hess et al ), some predictions of this theory were also published in the wake of the EHT publication.…”

“…Due to the property σ + σ − = 0, the representation in Equation (2) is called the zero‐divisor basis . For a consistent theory, one has to connect the two components by a constraint, which is discussed in Hess et al () and Hess & Greiner ()), requiring that the pc length element squared is real , where we defined the symmetric combination and antisymmetric one …”