Effect of Dark Energy in Geometrothermodynamics and Phase Transitions of Regular Bardeen AdS Black Hole

Abstract

We investigate thermodynamics and geometrothermodynamics of regular Bardeen -AdS black hole with quintessence. The thermodynamics of the black hole is studied using temperature-entropy (T-S) and Pressure -Volume (P-V) plots, which indicate critical behavior. This is also confirmed from the divergence of specific heat against entropy, which shows a second order phase transition. Using the concept of thermodynamic Ruppeiner and Weinhold geometry, we calculated the thermodynamic curvature scalar RR and RW in the quintessence dark energy regime. While these curvature scalars enable us to identify the critical behavior, they do not show divergence at the phase transition points observed in specific heat study. To resolve this puzzle we have adopted the method of geometrothermodynamics proposed by Hernando Quevedo. Choosing a Legendre invariant Quevedo metric, the curvature scalar RQ shows singularity at the same point as seen in the specific heat divergence.

Spatial and Temporal Chaos of a Bardeen-AdS Black Hole and Effects of Quintessence Dark Energy

“…A series of P − v criticality studies of black holes chemistry have pointed out that it is the horizon radius r h rather than the thermodynamic volume V that should be associated with the "fluid" volume [21][22][23][24][34][35][36]. So we abide by the same convention to define the specific volume v = 2r h .…”

“…In Refs. [34][35][36], quintessential Bardeen-AdS black holes have also been investigated successively. Based on these works, we attempt to test the chaotic behaviors in the extended phase space to find out how the quintessence exactly affects the black holes inside.…”

Comparison of thermodynamic behaviors of two regular-AdS black holes

“…Considering the magnetic charge as a minimum length of BH [42,43], it can be interpreted alternatively as a minimal cutoff length that makes gravity ultraviolet self-complete. We can re-written the equations (2) and (3) as ( )…”

Effects of global monopole on critical behaviors and microstructure of charged AdS black holes

“…Luckily, thermodynamic geometry is known as an elegant measure of global fluctuations in thermodynamic systems caused by interactions and available to give insight into the underlying statistical mechanical system [24][25][26][27]. It has been advanced as a useful tool for studying microscopic properties of black hole system and been extensively adopted [28][29][30][31][32][33][34][35][36].…”