Thermal aspects of central supermassive black holes in a fractal framework

In this paper we will compute the entropy of a supermassive black hole (SMBH) that dwells at the center of the galaxies described in an intricate, fractal, structure. We will consider that the dweller SMBH is of the power law kind introduced by Barrow recently. The entropy will be calculated from an expression that used the velocity dispersion and a specific parameter given by this power law entropy. This parameter, when different from zero and equal to a non-integer number, describes a more intricate structure of spacetime, namely, a fractal framework. We described the results of the entropic investigations of ten galaxies that are considered to live in a fractal structure as well. We have also computed other thermodynamical quantities like the temperature, the heat capacity, the Helmholtz free energy and the partition function. We have shown that in the case of a more intricate geometry, the Helmholtz free energy is negative meaning that the entropy is bigger than the internal energy. The results obtained here are within the expected results given by the Barrow BH entropic model.