  In this work, we present the thermodynamic study of a model that considers
the black hole as a condensate of gravitons. In this model, the spacetime is
not asymptotically flat because of a topological defect that introduces an
angle deficit in the spacetime like in Global Monopole solutions. We have
obtained a correction to the Hawking temperature plus a negative pressure
associated with the black hole of mass $M$. In this way, the graviton
condensate, which is assumed to be at the critical point defined by the
condition $\mu_{ch}$=0, has well-defined thermodynamic quantities $P$, $V$,
$T_{h}$, $S$, and $U$ as any other Bose-Einstein condensate (BEC). In addition,
we present a formal equivalence between the Letelier spacetime and the line
element that describes the graviton condensate. We also discuss the Kiselev
black hole, which can parametrize the most well-known spherically symmetric
black holes. Finally, we present a new metric, which we will call the
BEC-Kiselev solution, that allows us to extend the graviton condensate to the
case of solutions with different matter contents.
