Mechanisms behind the Aschenbach effect in non-rotating black hole spacetime

General relativity predicts that a rotating black hole drags the spacetime due to its spin. This effect can influence the motion of nearby objects, causing them to either fall into the black hole or orbit around it. In classical Newtonian mechanics, as the radius (r) of the orbit increases, the angular velocity ($\Omega$) of an object in a stable circular orbit decreases. However, Aschenbach discovered that for a hypothetical non-rotating observer, contrary to usual behavior, the angular velocity increases with radius in certain regions (Aschenbach, 2004). Although the possibility of observing rare and less probable ”rotational” behaviors in a rotating structure is not unlikely or impossible. However, observing such behaviors in a “static” structure is not only intriguing but also thought-provoking, as it raises questions about the factors that might play a role in such phenomena. In seeking answers to this question, various static models, particularly in the context of nonlinear fields, were examined, with some results presented as examples in the article. Among the models studied, the model of Magnetic Black Holes in 4D Einstein–Gauss–Bonnet Massive Gravity Coupled to Nonlinear Electrodynamics (M-EGB-Massive) appears to be a candidate for this phenomenon. In the analysis section, we will discuss the commonalities of this model with previous models that have exhibited this phenomenon and examine the cause of this phenomenon. Finally, we will state whether this phenomenon is observable in other black holes and, if not, why.