If the ratio of the Schwarzschild radius of a Macro Holeum to its bound state radius , namely, is greater than or equal to unity, then the Schwarzschild radius of the Macro Holeum is greater than its physical radius. Therefore the Macro Holeum is a black hole. We call such a Macro Holeum a Black Holeum and denote it as BH.
Recall that the properties of a Macro Holeum are given by the following equations:
Substituting the expressions for and into the Black Holeum condition , we obtain the condition for a Holeum to be a Black Holeum to be
It is interesting to note that this depends only on and ; the quantity does not matter here. For the ground state, which is characterized by , this reduces to
Now, the entropy of a black hole is given by
where is the Boltzmann constant, is the black hole’s surface area, and is the Planck length.
The Black Holeum’s entropy is given by
Thus, the expression for the entropy of a Black Holeum is
is the entropy of the individual MBHs that constitute the Macro Holeum.
Black Holeums are quantum black holes whose internal structure can be predicted by means of the quantities , , and . Black Holeums are an example of black holes with internal structure. Per the black hole no-hair theorem, one can argue that all macroscopic (non-MBH) black holes are Black Holeums. This has interesting implications for black hole physics. More on this later.
 L. K. Chavda and Abhijit L. Chavda, Dark matter and stable bound states of primordial black holes, arXiv:gr-qc/0308054 (2002).