Thermodynamics of conformal anomaly corrected black holes in AdS space

We present exact analytical black hole solutions with conformal anomaly in AdS space and discuss the thermodynamical properties of these black hole solutions. These black holes can have a positive, zero and negative constant curvature horizon, respectively. For the black hole with a positive constant curvature horizon, there exists a minimal horizon determined by the coefficient of the trace anomaly, the black hole with a smaller horizon is thermodynamically unstable, while it is stable for the case with a larger horizon. The Hawking–Page transition happens in this case. For the black hole with a Ricci flat horizon, the black hole is always thermodynamically stable and there is no Hawking–Page transition. In the case of the black hole with a negative constant curvature horizon, there exists a critical value for the coefficient of the trace anomaly, under this critical value, the black hole is always thermodynamical stable and the Hawking–Page transition does not happen. When the coefficient is beyond the critical value, the black hole with a smaller horizon is thermodynamically unstable, but it becomes stable for the case with a larger horizon, the Hawking–Page transition always happens in this case. The latter is a new feature for the black holes with a negative constant curvature horizon.