Thermodynamic geometry of charged dilaton black holes in AdS spaces

Abstract

It was shown that with the combination of three Liouville-type dilaton potentials, one can derive dilaton black holes in the background of anti-de-Sitter (AdS) spaces. In this paper, we further extend the study on the dilaton AdS black holes by investigating their thermodynamic instability through a geometry approach. First, we review thermodynamic quantities of the solutions and check the validity of the first law of thermodynamics. Then, we investigate phase transitions and stability of the solutions. In particular, we disclose the effects of the dilaton field on the stability of the black holes. We also employ the geometrical approach toward thermodynamical behavior of the system and find that the divergencies in the Ricci scalar coincide with roots and divergencies in the heat capacity. We find that the behavior of the Ricci scalar around divergence points depends on the type of the phase transition.

Brane universe and holography in the spacetime of a charged AdS dilaton black hole

“…By combining three different Liouville-type dilaton potentials, [38][39][40] obtains the asymptotically AdS black hole solution in Einstein-Maxwell-Dilaton theory. Basing on this black hole solution, many interesting physical phenomenology have been explored, like the black hole thermodynamics [41,42], holographic thermalization [43], black hole phase transition in extend phase space [44], and domain wall cosmology [45].…”

Phase structure and quasinormal modes of a charged AdS dilaton black hole

“…Ref. [20] explores phase transitions in this system by the method of thermodynamic geometries. In this method, divergences of the Ricci scalar coincide with the phase transition points of heat capacities.…”

“…In this method, divergences of the Ricci scalar coincide with the phase transition points of heat capacities. According to [20], the charged AdS dilaton black holes of [14] enjoy many phase transitions, among which one occurs between two stable black holes.…”

“…According to ref. [19,20] the charged dilaton black hole has rich structure of phases, even when the pressure effects are not considered. We expect that more interesting phase transitions will occur in this system when pressures are considered, just as pointed previously.…”

Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole

“…The geometry of AdS black hole thermodynamics has been extensively studied by several authors [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”