A few years back, J. D. Barrow questioned whether quantum gravitational phenomena may bring an intricate, fractal framework on the black hole (BH) horizon. The formulation of an entropic formula generalizing the Bekenstein–Hawking concept of entropy has a parameter that shows the framework in which the BH is embedded where, if it is equal to zero, it represents the standard flat structure, however, if it is equal to one it means that we have a fractal geometrization of the BH construction. In this paper, we will consider that this parameter, normally represented by Formula: see text, is dependent on the apparent horizon radius of the BH. Hence, we have modifications concerning the Friedmann equations. The objective is to be able to analyze the fractal effect at each point inside the event horizon, which is not allowed with a constant parameter.
Abreu et al. (Sat,) studied this question.