Thermodynamics of graviton condensate

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 $$\mu _{ch}=0,$$ μ ch = 0 , has well-defined thermodynamic quantities P, V, $$T_{h}$$ 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.