Charged AdS black hole and the quantum tunneling from black hole to white hole

Abstract: In this paper, we show that depending on the sign of the electric charge $Q$, the charged AdS black hole (BH) possesses two alternative facets when the cosmological constant is identified to the thermodynamic pressure $P$. It is discovered that: 1) the equation of state of BH corresponds to $Q>0$ and when $Q$ changes from $Q>0$ to $Q<0$ we obtain the equation of state (EOS) of white hole (WH); 2) Based on the WH equation of state we found the phase transition from small to large WHs which behaves like the liquid $-$ gas phase transition at negative temperature, $T<0$, and, at the same time, its entropy equals with minus sign the entropy of BH. As a consequence, the latent heat $\Delta H_{WH}(T)$ which releases in this process equals with minus sign the latent heat of BH, too; 3) Finally, the probability of the quantum tunneling from the BH to the WH is obtained. We suggest the perspective of application of the results above to the AdS/CFT duality.