# Predictions of the pseudo-complex theory of Gravity for EHT observations- II. Theory and predictions

## TL;DR

This paper explores pseudo-complex General Relativity, a modified gravity theory with two parameters, predicting distinctive dark and bright rings in black hole accretion disk images, relevant for EHT observations.

## Contribution

It introduces the theoretical framework of pseudo-complex GR with novel parameters and predicts observable features in black hole imaging.

## Key findings

- Predicts a dark ring followed by a bright ring in accretion disk emission profiles.
- Suggests dark energy accumulation affects light rings around black holes.
- Provides theoretical predictions for EHT observations based on modified gravity.

## Abstract

We present a resum\'e 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.