A note of the first law of thermodynamics by gravitational decoupling

Abstract

We provide a way of decoupling the first law of thermodynamics in two sectors : the standard first law of thermodynamics and the quasi first law of thermodynamics. It is showed that both sectors share the same thermodynamics volume and the same entropy. However, the total thermodynamics pressure, the total temperature and the total local energy correspond to a simple sum of the thermodynamics contributions of each sector. On the other hand, turning on the coupling constant α, the total energy, given by the Noether charge, increases proportionally to this constant. Furthermore, it is showed a simple example, where, there is a phase transition between stable/unstable black hole, and, due to the application of the decoupling, it is possible to determinate that the cause of this phase transition is the behavior of the temperature at the quasi sector.