GaussBonnet coupling constant as a free thermodynamical variable and the associated criticality
Abstract
The thermodynamic phase space of GaussBonnet (GB) AdS black holes is extended, taking the inverse of the GB coupling constant as a new thermodynamic pressure . We studied the critical behavior associated with in the extended thermodynamic phase space at fixed cosmological constant and electric charge. The result shows that when the black holes are neutral, the associated critical points can only exist in five dimensional GBAdS black holes with spherical topology, and the corresponding critical exponents are identical to those for the Van der Waals system. For charged GBAdS black holes, it is shown that there can be only one critical point in five dimensions (for black holes with either spherical or hyperbolic topologies), which also requires the electric charge to be bounded within some appropriate range; while in dimensions, there can be up to two different critical points at the same electric charge, and the phase transition can occur only at temperatures which are not in between the two critical values.
 Publication:

European Physical Journal C
 Pub Date:
 July 2014
 DOI:
 10.1140/epjc/s1005201429708
 arXiv:
 arXiv:1311.3053
 Bibcode:
 2014EPJC...74.2970X
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 23 pages. V2: modified all P_{GB}r_+ plots using dimensionless variables, added comments on the relationship to Einstein limit