No abstract

We obtain and analyze an exact solution to Einstein-Maxwell-scalar theory in (2+ 1) dimensions, in which the scalar field couples to gravity in a nonminimal way, and it also couples to itself with the self-interacting potential solely determined by the metric ansatz. A negative cosmological constant naturally emerges as a constant term in the scalar potential. The metric is static and circularly symmetric and contains a curvature singularity at the origin. The conditions for the metric to contain 0, 1 and 2 horizons are identified, and the effects of the scalar and electric charges on the size of the black hole radius are discussed. Under proper choices of parameters, the metric degenerates into some previously known solutions in (2 + 1)-dimensional gravity.

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 P GB . We studied the critical behavior associated with P GB 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 GB-AdS black holes with spherical topology, and the corresponding critical exponents are identical to those for the Van der Waals system. For charged GB-AdS 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 d > 5 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.

The extended thermodynamics of static charged AdS black holes in conformal gravity is analyzed. The P − V criticality of these black holes has some unusual features. There exists a single critical point with critical temperature T c and critical pressure P c . At fixed T > T c (or at fixed P > P c ), there are two zeroth order phase transition points but no first order phase transition points. The systems favors large pressure states at constant T , or high temperature states at constant P . arXiv:1405.7665v2 [gr-qc]