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 $$\alpha $$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.

Energy exchange between relativistic fluids: the polytropic case

“…where ζ < 0 is in agreement with (61), which indicates that A decreases as M increases [see Eq. ( 33) and ( 66)].…”

Gravitational decoupling for hairy black holes in asymptotic AdS spacetimes*

“…Finally, let us comment on some concrete prospects of this study. Currently, black hole thermodynamics in the presence of a negative cosmological constant is becoming even more appealing because they allow a gauge duality description through thermal field theory via the AdS/CFT correspondence [61]. The gravitational decoupling method has been applied to discuss the thermodynamics of spherically symmetric black holes in asymptotically flat spacetime [62], where the first law of thermodynamics was decoupled into two sectors: the standard first law of thermodynamics and the quasi first law of thermodynamics.…”

A new exact solution of black-strings-like with a dS core

“…A complete analysis of the solution can be viewed in reference [17]. See also [24,26] for a thermodynamics analysis .…”