P-V criticality of charged dilatonic black holes

TL;DR

This paper explores the phase transition and critical behavior of charged dilatonic black holes in Einstein-Maxwell-dilaton gravity with non-standard asymptotics, revealing universal critical exponents and conditions for physical critical points.

Contribution

It introduces a new analysis of P-V criticality for charged dilatonic black holes with Liouville potentials, deriving a Smarr relation and examining the universality of critical exponents.

Findings

Critical values are physical when dilaton coupling < 1 and horizon is spherical.

Critical exponents are universal and independent of system details.

The volume differs from the geometrical volume in these black holes.

Abstract

In this paper, we investigate the critical behavior of charged black holes of Einstein-Maxwell-dilaton gravity in the presence of two Liouville-type potentials which make the solution asymptotically neither flat nor AdS and has a parameter $% \Lambda $ treated as a thermodynamic quantity that can vary. We obtain a Smarr-type relation for charged dilatonic black holes and find out that the volume is different from the geometrical volume. We study the analogy of the Van der Waals liquid-gas system with the charged dilatonic black hole system while we treat the black hole charge as a fixed external parameter. Moreover, we show that the critical values for pressure, temperature and volume are physical provided the coupling constant of dilaton gravity is less than one and the horizon is sphere. Finally, we calculate the critical exponents and show that they are universal and are independent of the details of the system although the thermodynamic quantities depend on the dilaton parameter and the dimension of the spacetime.