Thermodynamics of spinning AdS4 black holes in gauged supergravity

In this paper we study the thermodynamics of rotating black hole solutions arising from four-dimensional gauged N=2 supergravity. We analyze two different supergravity models, characterized by prepotentials $F = -i X^0 X^1$ and $F= -2i \sqrt{X^0 (X^1)^3}$. The black hole configurations are supported by electromagnetic charges and scalar fields with different kinds of boundary conditions. We perform our analysis in the canonical ensemble, where we find a first order phase transition for a suitable range of charges and angular momentum. We perform the thermodynamic stability check on the configurations. Using the holographic dictionary we interpret the phase transition in terms of expectation values of operators in the dual field theory, which pertains to the class of ABJM theories living on a rotating Einstein universe. We extend the analysis to dyonic configurations as well. Lastly, we show the computation of the on-shell action and mass via holographic renormalization techniques.