Critical phenomena in Born-Infeld AdS black holes

TL;DR

This paper explores the critical thermodynamic behavior of Born-Infeld AdS black holes, calculating critical exponents and verifying scaling laws, with implications for related Reissner Nordstrom AdS black holes.

Contribution

It provides a detailed analysis of critical phenomena and exponents in Born-Infeld AdS black holes, confirming thermodynamic scaling laws and the GHF hypothesis.

Findings

Critical exponents satisfy thermodynamic scaling laws.

GHF hypothesis is compatible with the scaling laws.

Results extend to Reissner Nordstrom AdS black holes in certain limits.

Abstract

We investigate the thermodynamics of critical phenomena in Born-Infeld AdS black holes using a canonical ensemble. The critical behavior has been studied near the critical point which is characterized by a discontinuity in the heat capacity at constant charge. We explicitly calculate the critical exponents of the relevant thermodynamic quantities. These exponents satisfy all the thermodynamic scaling laws. We also check the Generalized Homogeneous Function (GHF) hypothesis (or the scaling hypothesis) which is shown to be compatible with the thermodynamic scaling laws. Finally we check the validity of the scaling laws of second kind which include the critical exponents associated with the spatial correlation. In the appropriate limit our results also provide the corresponding expressions for the Reissner Nordstrom AdS case.